2. 2007,1- حركة في منزلق مائي
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لإيجاد مقدار السرعة في لحظة معينة ، يجب حساب متوسط السرعة بين اللحظة السابقة واللحظة التي تليها.
نحسب متوسط السرعة من اللحظة t = 1.2s حتى اللحظة t = 2s.
متوسط هذه السرعة يساوي تقريبًا السرعة في منتصف الفترة الزمنية أي في اللحظة t = 1.6s:
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מהירות ממוצעת זו שווה בקירוב למהירות באמצע הזמן ברגע t=1.6s :
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متوسط السرعة يساوي بالضبط السرعة في منتصف الفترة الزمنية للحركة فقط إذا كان الجسم يتحرك في حالة تسارع ثابت، وإلا فإن متوسط السرعة يساوي تقريبًا السرعة اللحظية في منتصف الفترة.
عند حساب متوسط السرعة ، كلما كان زمن الحركة أقصر ، كانت قيمة التقريب أفضل.
בחישוב המהירות הממוצעת ככל שזמן התנועה יותר קטן , כך ערך הקירוב טוב יותר.
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يجب تكرار حساب متوسط السرعة لأزمنة الحركة ، على غرار القسم السابق ، لبقية أزمنة الحركة المطلوبة.
نحسب متوسط السرعات التي يمكننا من خلالها إيجاد السرعات اللحظية في جميع الأزمنة المطلوبة:
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«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«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»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»26«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»7«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»22«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»04«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»8«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»05«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»13«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»08«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»88«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»8«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»25«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»
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نركّز قيم السرعات المحسوبة في جدول:
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في السؤال مكتوب أنك لست مطالبًا أن تُفصّل، لكن لا يمكن إيجاد السرعات اللحظية دون حساب.
هذا هو السبب في أنه من الأفضل عدم الاهتمام إلى هذه التعليمات وحساب السرعة بطريقة منظمة وكاملة ومفصلة في كل لحظة.
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يجب رسم الرسم البياني للسرعة كدالة للزمن، وفقًا للبيانات الواردة في الجدول في القسم السابق.
نصف قيم الجدول من القسم السابق في رسم بياني للسرعة كدالة لزمن:
1. في السؤال ، مكتوب يجب رسم "مقدار السرعة" كل رسم بياني للسرعة كدالة للزمن، يصف مقدار السرعة فقط كدالة للزمن.
2. الرسم البياني ليس خطيًا ، من المهم عدم إضافة الخط المستقيم الأكثر احتمالاً (خط الاتجاه).
3. كما هو الحال دائمًا ، لا تنسى أسماء المحاور ووحداتها.
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نعم
يصف التسارع المماسي التسارع في اتجاه مماس للمسار، وهذا التسارع يسبب تغييرًا في مقدار السرعة.
نعم. وفقًا لقيم السرعات اللحظية التي حسبناها، يمكن ملاحظة أن سرعة سعاد متغيرة المقدار، وبالتالي هناك تسارع مماسي لها.
يصف التسارع المماسي التغيير في مقدار السرعة، سواء كانت السرعة تتزايد أو تتناقص.
لا يوجد تباطؤ مماسي، ولا يساهم مفهوم التباطؤ في فهم المبادئ، يوصى بعدم استخدام مفهوم التباطؤ.
לא קיימת תאוטה משיקית, מושג התאוטה לא תורם להבנת העקרונות , מומלץ לא להשתמש במושג התאוטה.
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نعم
يصف التسارع المركزي (الراديالي) التسارع في اتجاه عمودي على اتجاه مسار الحركة، وهذا التسارع يسبب تغيرًا في اتجاه متجه السرعة، وتغيرًا في اتجاه الحركة.
نعم. مكتوب أن الزلاجّة لها شكل منحني، لذلك أثناء حركة سعاد يتغير اتجاه الحركة، وبالتالي يكون هناك تسارع راديالي (نحو المركز).
للإجابة على هذا السؤال بشكل صحيح ، يجب الانتباه إلى حقيقة أن الزلاجّة منحنية.
من المهم أن نفهم تمامًا معنى التسارع الراديالي، بحيث يسهل علينا الانتباه، وإذا لم ننتبه، على الأقل سنعرف ما الذي نبحث عنه.
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