حلول التدريبات العملية بالكينماتيكا على خط مستقيم 1- الدوال
| الموقع: | YouCube |
| المقرر: | קינמטיקה בקו ישר - ערבית |
| كتاب: | حلول التدريبات العملية بالكينماتيكا على خط مستقيم 1- الدوال |
| طبع بواسطة: | משתמש אורח |
| التاريخ: | الأربعاء، 4 فبراير 2026، 2:36 AM |
1. الحركة بسرعة ثابتة
1.1.
يتحرك الجسم بسرعة ثابتة ، نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«/math»
نستخدم دالة الموقع كدالة للزمن المناسبة للحركة بسرعة ثابتة.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
نعوض معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»11«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
1.2.
يتحرك الجسم بسرعة ثابتة، سرعته سالبة، ويتحرك عكس اتجاه الحركة.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«/math»
نستخدم دالة الموقع كدالة للزمن المناسبة للحركة بسرعة ثابتة.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
نعوض معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
1.3.
يتحرك الجسم بسرعة ثابتة ، نكتب بيانات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نستخدم دالة الموقع كدالة للزمن المناسبة للحركة بسرعة ثابتة.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
نعبر عن زمن حركة الجسم، نعوض معطيات الحركة في التعبير الناتج:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»X«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mrow»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»V«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»8«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»S«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«msub»«mi mathvariant=¨bold-italic¨»s«/mi»«mrow/»«/msub»«/menclose»«/mstyle»«/math»
1.4.
يتحرك الجسم بسرعة ثابتة ، نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«/math»
نستخدم دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
نعبر عن الموقع الابتدائي، ونعوض معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«msub»«mi mathvariant=¨bold¨»X«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
1.5.
يتحرك الجسم بسرعة ثابتة، نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نستخدم دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
نعبر عن سرعة الجسم، ونعوض معطيات الحركة في التعبير الذي حصلنا عليه:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»X«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mrow»«mi mathvariant=¨bold¨»t«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»8«/mn»«/mrow»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mfrac»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/menclose»«/mstyle»«/math»
2. جسمان يتحركان بسرعة ثابتة بأزمنة حركية متساوية
2.1.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لايجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msub»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»s«/mi»«/msub»«/menclose»«/mstyle»«/math»
نعوض الزمن في إحدى دالتي الموقع كدالة للزمن (يمكن تعويضه في أي من الدالتين)، ونجد موقع الالتقاء 'X:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»12«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
2.2.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msub»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»s«/mi»«/msub»«/menclose»«/mstyle»«/math»
نعوض الزمن في إحدى دالتي الموقع كدالة للزمن (يمكن تعويضه في أي من الدالتين)، ونجد موقع الالتقاء 'X:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
2.3.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»13«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»13«/mn»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»384«/mn»«mi mathvariant=¨bold-italic¨»s«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض الزمن في إحدى دالتي الموقع كدالة للزمن (يمكن تعويضه في أي من الدالتين)، ونجد موقع الالتقاء 'X:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»384«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»46«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»46«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
2.4.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»13«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»13«/mn»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»384«/mn»«mi mathvariant=¨bold-italic¨»s«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض الزمن في إحدى دالتي الموقع كدالة للزمن (يمكن تعويضه في أي من الدالتين)، ونجد موقع الالتقاء 'X:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»384«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»53«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»53«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
2.5.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»13«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»5«/mn»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»13«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»384«/mn»«mi mathvariant=¨bold-italic¨»s«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لحظة إلقاء الجسمين سالبة، وبالتالي يمكن تحديد أن الجسمين لا يلتقيان.
2.6.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»0«/mn»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi»§#1581;§#1604;«/mi»«mo»§#160;«/mo»«mi»§#1610;§#1608;§#1580;§#1583;«/mi»«mo»§#160;«/mo»«mi»§#1604;§#1575;«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لا يوجد حل رياضي ، لذلك يمكن أن نجزم بأن الجسمين لا يلتقيان.
2.7.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
تتحققق المعادلة لكل قيمة لـ 't ، لذلك يمكن القول أن الجسمين يلتقيان في كل لحظة.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»§#1604;§#1581;§#1592;§#1577;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1603;§#1604;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1601;§#1610;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1610;§#1604;§#1578;§#1602;§#1610;§#1575;§#1606;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1575;§#1604;§#1580;§#1587;§#1605;§#1575;§#1606;«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض الزمن في إحدى دالتي الموقع كدالة للزمن (يمكن تعويضه في أي من الدالتين)، ونجد موقع الالتقاء 'X:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
تلتقي الجسمان في كل لحظة، لذلك يلتقيان أيضًا في كل مكان.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»§#1605;§#1603;§#1575;§#1606;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1603;§#1604;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1601;§#1610;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1575;§#1604;§#1580;§#1587;§#1605;§#1575;§#1606;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1610;§#1604;§#1578;§#1602;§#1610;«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
2.8.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع ونجد زمن الالتقاء 't:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»18«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»0«/mn»«mn mathvariant=¨bold¨»18«/mn»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mi mathvariant=¨bold-italic¨»s«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض الزمن في إحدى دالتي الموقع كدالة للزمن (يمكن تعويضه في أي من الدالتين)، ونجد موقع الالتقاء 'X:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
3. جسمان يتحركان بسرعة ثابتة بزمني حركة مختلفين
3.1.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لم يبدأ الجسمان بالتحرك معًا في نفس اللحظة، زمن حركة الجسمين من لحظة بداية حركتهما حتى لحظة التقائهما، مختلف!
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين بدلالة زمن حركة كل منهما:
دالة الموقع كدالة للزمن الملائمة للحركة
بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»5«/mn»«/menclose»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
حصلنا على معادلة واحدة بمجهولين، لإيجاد زمن الالتقاء ، نكتب معادلة أخرى: معادلة الفرق بين زمني الحركة.
بدأ الجسم 2 يتحرك قبل 10 ثوانٍ من حركة الجسم 1. لذلك، في أي لحظة أثناء حركة الجسمين، يكون زمن حركة الجسم 2 أكبر بـ 10 ثوانٍ من زمن حركة الجسم 1 ، وهذا أيضًا صحيح بالنسبة للحظة الالتقاء. لذلك يتحقق: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»10«/mn»«/menclose»«/mstyle»«/math»
نحل هيئة معادلتين بمجهولين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض 't2 في المعادلة الأولى :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»10«/mn»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»25«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»25«/mn»«mn mathvariant=¨bold¨»7«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»57«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
نحسب زمن حركة الجسم الثاني من لحظة بداية حركته حتى لحظة الالتقاء:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»57«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»13«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»57«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
للتلخيص زمني حركة الجسمين منذ لحظة بداية حركتهما حتى لحظة التقائهما :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨28px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»57«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»13«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»57«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
لايجاد موقع الالتقاء، نعوض أحد زمني الالتقاء في دالة الموقع كدالة للزمن المناسبة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»57«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»35«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
لذلك، يلتقي الجسمان في الموقع X = 35.14 مترًا بعد مضي 3.57 ثانية من لحظة بداية حركة الجسم 1، وبعد مضي 13.57 ثانية من اللحظة التي يبدأ فيها الجسم 2 في الحركة.
3.2.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لم يبدأ الجسمان بالتحرك معًا في نفس اللحظة، زمن حركة الجسمين من لحظة بداية حركتهما حتى لحظة التقائهما، مختلف!
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين بدلالة زمن حركة كل منهما:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع كدالة للزمن ونجد زمني الالتقاء 't1' t2: :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»5«/mn»«/menclose»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
حصلنا على معادلة واحدة بمجهولين، لإيجاد زمن الالتقاء، نكتب معادلة أخرى: معادلة الفرق بزمني الحركة.
بدأ الجسم 1 يتحرك قبل ثانية من بداية حركة الجسم 2. لذلك، في أي لحظة أثناء حركة الجسمين، يكون زمن حركة الجسم 2 أكبر بثانية واحدة من زمن حركة الجسم 1، وهذا أيضًا صحيح بالنسبة للحظة الالتقاء. لذلك يتحقق: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/menclose»«/mstyle»«/math»
نحل هيئة معادلتين بمجهولين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض 't1 من المعادلة الثانية في المعادلة الأولى :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#FF0000¨»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»11«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
نحسب زمن حركة الجسم الأول منذ لحظة بداية حركته حتى لحظة الالتقاء:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
للتلخيص زمني حركة الجسمين من لحظة بداية حركتهما حتى لحظة التقائهما :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨28px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
لايجاد موقع الالتقاء، نعوض أحد زمني الالتقاء في دالة الموقع كدالة للزمن المناسبة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»54«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
لذلك، يلتقي الجسمان في الموقع X=5.54m بعد مضي 1.27 ثانية منذ لحظة بداية حركة الجسم 1، وبعد مضي 0.27 ثانية منذ اللحظة التي يبدأ فيها الجسم 2 في الحركة.
3.3.
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لم يبدأ الجسمان بالتحرك معًا في نفس اللحظة، زمن حركة الجسمين من لحظة بداية حركتهما حتى لحظة التقائهما، مختلف!
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين بدلالة زمن حركة كل منهما:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع كدالة للزمن ونجد زمني الالتقاء 't1' t2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»5«/mn»«/menclose»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
حصلنا على معادلة واحدة بمجهولين، لإيجاد زمن الالتقاء، نكتب معادلة أخرى: معادلة الفرق بزمني الحركة.
بدأ الجسم 1 يتحرك قبل ثانية من بداية حركة الجسم 2. لذلك، في أي لحظة أثناء حركة الجسمين، يكون زمن حركة الجسم 2 أكبر بثانية واحدة من زمن حركة الجسم 1 ، وهذا أيضًا صحيح بالنسبة للحظة الالتقاء. لذلك يتحقق: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/menclose»«/mstyle»«/math»
נنحل هيئة معادلتين بمجهولين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض 't1 من المعادلة الثانية في المعادلة الأولى :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#FF0000¨»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«mn mathvariant=¨bold¨»11«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»36«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
نظرًا لأن أحد زمني الالتقاء سالب، فيمكن تحديد أن الجسمين لا يلتقيا أثناء حركتهما!
3.4.
يلتقي الجسمان مرتين، المرة الأولى عندما يكون الجسم 2 في حالة سكون، ومرة أخرى عندما يكون الجسم 2 في حالة حركة.
لايجاد زمني الالتقاء، يجب عليك تكرار جميع الخطوات لايجاد زمن وموقع الالتقاء مرتين.
نجد زمن وموقع الالتقاء الأول (عندما يكون الجسم 2 في حالة سكون):
نكتب معطيات حركة الجسمين في هذه الحالة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نكتب دالة الموقع كدالة للزمن للجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/menclose»«/mstyle»«/math»
نقارن بين دالتي الموقع ونجد زمن الالتقاء:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لايجاد موقع الالتقاء الأول، نعوض زمن حركة الجسم 1 حتى االالتقاء في دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
يلتقي الجسمان لأول مرة في الموقع الذي يستقر فيه الجسم 2 ، في الموقع X = 8 م.
نجد زمن وموقع الالتقاء الثاني (عندما يكون الجسم 2 في حالة حركة):
نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لم يبدأ الجسمان بالتحرك معًا في نفس اللحظة، زمن حركة الجسمين من لحظة بداية حركتهما حتى لحظة التقائهما، مختلف!
لإيجاد زمن وموقع الالتقاء، نكتب دالة الموقع كدالة للزمن لكل من الجسمين بدلالة زمن حركة كل منهما:
دالة الموقع كدالة للزمن الملائمة للحركة بسرعة ثابتة: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 1:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالة الموقع كدالة للزمن للجسم 2
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/menclose»«/mstyle»«/math»
في لحظة الالتقاء، قيمة موقع الجسمين متساوٍ. نقارن بين دالتي الموقع كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»5«/mn»«/menclose»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
حصلنا على معادلة واحدة بمجهولين، لإيجاد زمن الالتقاء ، نكتب معادلة أخرى: معادلة الفرق بين زمني الحركة.
بدأ الجسم 1 يتحرك قبل 10 ثوانٍ من حركة الجسم 2. لذلك، في أي لحظة أثناء حركة الجسمين، يكون زمن حركة الجسم 1 أكبر بـ 10 ثوانٍ من زمن حركة الجسم 2 ، وهذا أيضًا صحيح بالنسبة للحظة الالتقاء. لذلك يتحقق: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»10«/mn»«/menclose»«/mstyle»«/math»
نحل هيئة معادلتين بمجهولين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«/mrow»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض 't1 في المعادلة الأولى :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#FF0000¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»15«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»15«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»7«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
نحسب زمن حركة الجسم 1 من لحظة بداية حركته حتى لحظة الالتقاء:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
للتلخيص زمني حركة الجسمين منذ لحظة بداية حركتهما حتى لحظة التقائهما :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨28px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
لايجاد موقع الالتقاء، نعوض أحد زمني الالتقاء في دالة الموقع كدالة للزمن الملائمة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»14«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
لذلك، يلتقي الجسمان في الموقع X=27.2m بعد مضي 12.41 ثانية من لحظة بداية حركة الجسم 1،
لتلخيص:
يلتقي الجسمان مرتين:
المرة الأولى: بعد 2.5 ثانية من بدء حركة الجسم 1، يكون الجسم 2 في حالة سكون.
والمرة الثانية: بعد 12.14 ثانية من اللحظة التي يبدأ فيها الجسم 1 بالتحرك، يكون الجسم 2 في حالة حركة
4. الحركة بتسارع ثابت
4.1.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
يتحرك الجسم بتسارع ثابت، نستخدم دالة الموقع كدالة للزمن :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/mstyle»«/math»
نعوض معطيات الحركة ونجد موقع الجسم في اللحظة t=6s :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»38«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«/mstyle»«/math»
4.2.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
يتحرك الجسم بتسارع ثابت، نستخدم دالة الموقع كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mstyle»«/math»
نعوض معطيات الحركة ونجد موقع الجسم في اللحظة t=6s :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mfrac»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/menclose»«/mstyle»«/math»
4.3.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
السؤال لا يتناول زمن الحركة، في مثل هذه الحالات يكون من المناسب استخدام تعبير مربع السرعات:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«mn mathvariant=¨bold¨»0«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
نجد الموقع النهائي باستخدام تعريف الازاحة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
طريقة أخرى: ايجاد زمن الحركة باستخدام دالة السرعة كدالة للزمن، ثم تعويض زمن الحركة في دالة الموقع كدالة للزمن.
نجد زمن حركة الجسم باستخدام دالة السرعة كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mrow»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mrow»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
نجد موقع الجسم في اللحظة t = 3s ، بمساعدة دالة الموقع كدالة للزمن الملائمة للحركة بتسارع ثابت:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/mrow»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
4.4.
يتحرك الجسم ذهابًا وإيابًا، وفي نهاية حركته يعود إلى نقطة بداية الحركة، وتكون الإزاحة مساوية لصفر.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#9651;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
يتحرك الجسم بتسارع ثابت، والموقع النهائي يساوي الموقع الابتدائي. نستخدم دالة المكان كدالة للزمن،
نعبر عن زمن حركة الجسم:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/mrow»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«menclose notation=¨downdiagonalstrike¨ mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«/menclose»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mrow»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نعوض معطيات الحركة ونجد زمن حركة الجسم:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mrow»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»6«/mn»«mi mathvariant=¨bold¨»s«/mi»«/menclose»«/mstyle»«/math»
طريقة أخرى: نحسب زمن حركة الجسم باستخدام دالة السرعة كدالة للزمن: من تعبير مربع السرعات عندما تكونإزاحة الجسم المتحرك بتسارع ثابت تساوي صفرًا، يكون للجسم سرعتان:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#177;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
تكون سرعة الجسم في بداية الحركة «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math» ، وفي نهاية الحركة تكون سرعة الجسم«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»
نجد سرعة الجسم باستخدام دالة السرعة كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/mrow»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»6«/mn»«mi mathvariant=¨bold¨»s«/mi»«/menclose»«/mstyle»«/math»
4.5.
يتحرك الجسم ذهابًا وإيابًا ، وفي نهاية حركته لا يعود إلى نقطة بداية الحركة.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نكتب دالة الموقع كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/mrow»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نجد حلول المعادلة التربيعية:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«msup»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»6«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»1«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»73«/mn»«/mrow»«mn mathvariant=¨bold¨»1«/mn»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
يمر الجسم مرتين في الموقع x = 5m في المرة الأولى باللحظة t = 1.27s ومرة أخرى باللحظة t = 4.73s.
4.6.
يتحرك الجسم ذهابًا وإيابًا ، وفي نهاية حركته لا يعود إلى نقطة بداية حركته.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
يتحرك الجسم بتسارع ثابت، وزمن الحركة غير معطى في السؤال. نستخدم تعبير مربع السرعات:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»X«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»6«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
يمر الجسم مرتين في الموقع X=5m، في المرة الأولى كانت سرعته«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mstyle»«/math», في المرة الثانية سرعته«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mstyle»«/math».
طريقة أخرى: يمكن استخدام دالة السرعة كدالة للزمن، وتعويض زمني الحركة (من البند 5 د) اللذان يمر فيهما الجسم في الموقع X=5m.
نجد زمن حركة الجسم باستخدام دالة السرعة كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mrow»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
4.7.
يتحرك الجسم نحواليمين ، ويتوقف توقفًا لحظيًا في الموقع X=6.5m، ويعود إلى اليسار. لا يمر الجسم في الموقع X=8m.
نكتب معطيات الحركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نستخدم مبادئ الكينماتيكا لإيجاد زمن حركة الجسم من اللحظة التي تبدأ فيها الحركة حتى يصل إلى الموقع X=8m.
نستخدم دالة المكان كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«msup»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»6«/mn»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»12«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»1«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»1«/mn»«/mfrac»«/mstyle»«/math»
رياضيًا لا يمكن إجراء عملية جذر لقيمة سالبة. لذلك، لا توجد حلول للمعادلة.
لا توجد حلول لأن هذه الحركة مستحيلة. لا يصل الجسم إلى الموقع X=8m.
4.8.
يتحرك الجسم نحو اليمين ، ويتوقف توقفًا لحظيًا في الموقع X=6.5m ، ويعود إلى اليسار. يمر الجسم مرة واحدة فقط في الموقع X = 1m.
نكتب معطيات الجركة:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»?«/mo»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نستخدم دالةة الموقع كدالة للزمن لإيجاد زمن حركة الجسم من اللحظة التي يبدأ فيها حركته حتى وصوله إلى الموقع X=1m.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«msup»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«msup»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mstyle»«/math»
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الحل السالب غير ملائم ليكون زمن الحركة ، فالجسم يمر مرة واحدة فقط في الوقع X=1m باللحظة t=6.31s.
4.9.
يتحرك الجسم بتسارع سالب حتى يتوقف في الموقع X=8m ..
نكتب معطيات الحركة:
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يتحرك الجسم بتسارع ثابت، زمن الحركة غير معطى في السؤال ، نستخدم تعبير تربيع السرعات:
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5. جسمان يتحركان بحركات مختلفة
5.1.
يتحرك جسمان بحركات مختلفة ، يتحرك الجسم 1 نحو اليمين بسرعة آخذة بالنقصان، يتوقف ومن ثم يتحرك إلى اليسار.
يتحرك الجسم 2 بسرعة ثابتة وصغيرة نسبيًا إلى اليمين، اعتمادًا على الموقع الابتدائي للجسمين وحركتهما يبدو أنهما يلتقيان مرتين.
نكتب معطيات حركة المرور لكل من الهيئتين:
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نكتب لكل جسم دالة المكان كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»20«/mn»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msup»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
في لحظة الالتقاء 't، يكون موقع الجسمين هو نفسه، ويتحقق: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math».
حتى نجد زمن الالتقاء 't ، نقارن بين دالتي الموقع كدالة للزمن.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نرتب المعادلة التربيعية ونجد حلولها:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»19«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»19«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«msup»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»19«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»19«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mn mathvariant=¨bold¨»361«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»20«/mn»«/msqrt»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»19«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mn mathvariant=¨bold¨»18«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»46«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
خلاصة: في اللحظة التي تبدأ فيها الحركة، يتحرك الجسمان في نفس الاتجاه، ويلحق الجسم 1 بالجسم 2 بعد مضي 2 0.27 ثانية.
يلتقي الجسمان مرة أخرى بعد مضي 18.73 ثانية من بدء حركتهما ، عندما يتحرك الجسم 1 إلى اليسار ، ويتحرك الجسمان في اتجاهين متعاكسين.
5.2.
يلتقي الجسمان مرتين، حتى نجد موقعي الالتقاء، نعوض زمني الالتقاء في إحدى الدالتين:
نحسب موقع الالتقاء الأول:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»27«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
نحسب موقع الالتقاء الثاني:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»26«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»73«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
خلاصة: المرة الأولى التي يلتقي فيها الجسمان في الموقع X=8.27m، والمرة الثانية يلتقي الجسمان في الموقعX=26.73m
5.3.
وجدنا زمني التقاء الجسمين في البند 5.1 ، نستخدم دالة السرعة كدالة للزمن لإيجاد سرعة الجسم 1 في كل التقاء:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/mrow»«mo mathcolor=¨#0000FF¨»`«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»267«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»267«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»19«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»46«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«mo mathcolor=¨#0000FF¨»`«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»18«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»733«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»733«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»17«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»46«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»19«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»46«/mn»«mstyle mathvariant=¨bold¨ displaystyle=¨false¨»«mfrac»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«/menclose»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»`«/mo»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»17«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»46«/mn»«mstyle mathvariant=¨bold¨ displaystyle=¨false¨»«mfrac»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«/menclose»«/mstyle»«/math»
5.4.
يتحرك كلا الجسمين بتسارع، والجسم 1 يتحرك نحو اليمين بسرعة آخذة بالنقصان (تسارع سالب) ، يتوقف لحظيًا ثم ويعود إلى اليسار.
يتحرك الجسم 2 إلى اليسار بسرعة آخذة بالازدياد (تسارع موجب) ، يتوقف لحظيًا ثم يعود إلى اليمين.
يلتقي الجسمين مرتين، نكتب معطيات حركة الجسمين:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»02«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نكتب دالة المكان كدالة للزمن لكل جسم :
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mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msup»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»01«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msup»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
يكون موقع الجسمين في لحظة الالتقاء 't هو نفسه, ويتحقق: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math».
حتى نجد زمن الالتقاء 't نقارن بين دالتي الموقع كدالة للزمن.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/mrow»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
نجد حلول المعادلة التربيعية:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«msup»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mn mathvariant=¨bold¨»400«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»40«/mn»«/msqrt»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mn mathvariant=¨bold¨»18«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»97«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»25«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»74«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/mstyle»«/math»
خلاصة: يتحرك الجسمان في البداية باتجاه بعضهما البعض ويلتقيان بعد مضي 0.25 ثانية، وبعد ذلك تقل سرعة كل من الجسمين، وتوقف الجسان توقفًا لحظيًا، وتعود لتلتقي مرة أخرى للمرة الثانية ، بعد مضي 9.74 ثانية من لحظة بداية حركتهما.
5.5.
حتى نجد المواقع التي يلتقي فيها الجسمان، نعوض زمن حركة الجسمين حتى لحظة الالتقاء في إحدى دالتي المكان كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»`«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/mstyle»«/math»
نُشير لموقع الالتقاء الأول بـ «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»§#1488;«/mi»«/mrow»«/msub»«/mstyle»«/math» ولموقع الالتقاء الثاني بـ «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»§#1489;«/mi»«/mrow»«/msub»«/mstyle»«/math».
نجد موقع الالتقاء الأول:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»X«/mi»«mrow»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»§#1488;«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»25«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»25«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«msup»«mn mathvariant=¨bold¨»25«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0625«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
نجد موقع الالتقاء الثاني:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»X«/mi»«mrow»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»§#1489;«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»74«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»74«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»9«/mn»«mo mathvariant=¨bold¨».«/mo»«msup»«mn mathvariant=¨bold¨»74«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»97«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»94«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»86«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»
يلتقي الجسمان مرتين في نفس المكان بالضبط ، في الموقع X=5.5m.
5.6.
نُشير إلى اللحظة التي تكون فيها سرعة الجسمين متساوية بـ *t, في هذه اللحظة يتحقق:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
نكتب دالة السرعة كدالة للزمن للجسم 2:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
باللظة *t تكون سرعة الجسمين متساوية, نقارن بين تعبيري سرعة الجسمين ونجد *t:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»*«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
لذلك ، بعد مضي 5 ثوانٍ من بدء حركة كل من الجسمين، تكون سرعتهما متساوية.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»*«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»s«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
5.7.
السرعة هي نفسها من حيث المقدار عندما يتحرك الجسمان في نفس اتجاه الحركة وأيضًا عندما تحركان في اتجاهين متعاكسين.
تناولنا في البند السابق الحالات التي يتحرك فيها الجسمان في نفس اتجاه الحركة (رأينا أنه في هذه الحالة، يحدث هذا فقط عندما يتوقف الجسمان توقفًا لحظيًا).
نُشير لهذا الزمن بـ «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«/msup»«/mstyle»«/math» , في هذا الزمن يتحقق:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/mstyle»«/math»
دالتي السرعة كدالة للزمن:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»t«/mi»«/menclose»«/mstyle»«/math»
نقارن بين هاتين الدالتين ونجد «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«/msup»«/mstyle»«/math»:
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رياضيا يمكن ملاحظةأنه لكل قيمة لـ«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨24px¨»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«/msup»«/mstyle»«/math» سوف تتحقق المعادلة, لذلك ، في كل لحظة تكون سرعة كل من الجسمين متساوية المقدار.
وذلك لأن السرعة الابتدائية لكل منهما متساوية في المقدار والتسارع أيضًا بنفس المقدار. لذلك في كل لحظة تكون السرعة متساوية في المقدار.