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حسب ميل الرسم البياني. معنى الجملة: تزيد السرعة كل ثانية بمقدار ثابت مقداره مترين في الثانية.
في الرسم البياني للسرعة كدالة للزمن، فميل الرسم البياني يمثل التسارع. يجب معرفة معنى التسارع. يصف التسارع مقدار تغيير السرعة خلال كل ثانية.
نحسب ميل الرسم البياني:
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دلالة الجملة: " تسارع الدراجة النارية 2 متر في الثانية مربعة " هو أن سرعة الدراجة النارية تزداد كل ثانية بمقدار مترين في الثانية.
زادت سرعة الدراجة النارية لمدة 15 ثانية بمقدار 30 مترًا في الثانية.
كل مصطلح فيزيائي له معنى ، من المهم أن نفهم معنى جميع المصطلحات الفيزيائية. يمكن فهم معنى كل مصطلح فيزيائي حسب تعريفه.
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يمكن إيجاد تسارع السيارة في الفترة الزمنية الواردة في السؤال عن طريق حساب ميل الدالة في تلك الفترة الزمنية.
في التمثيل البياني للسرعة كدالة زمنية ، يكون ميل الرسم البياني مساويًا لتسارع الجسم. نجد ميل الرسم البياني في الفترة الزمنية بين t = 5s t = 15s.
بكلمات أخرى ، نستخدم تعريف التسارع:
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يظهر بين قوسين بالنسبة للمحور المحدد ، لأن اتجاه محور الحركة يؤثر على إشارة التسارع. يصف الرسم البياني السرعة بالنسبة للمحور المحدد ، وبالتالي فإن التسارع الذي تم الحصول عليه من حساب الميل في الرسم البياني هو أيضًا متعلق بالمحور المحدد.
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في اللحظة t = 15 ثانية ، الدراجة النارية تسبق السيارة.
معطي الموقع البدائي لكل مركبة في السؤال ، بمساعدة الرسم البياني يمكنك إزاحة كل من المركبتين. بمساعدة المواقع الابتدائية والإزاحة يمكن إيجاد الموقع باللحظة t = 15s.
الموقع الابتدائي للدراجة النارية هو X0=30m. والموقع الابتدائي للسيارة هو X0 = 0m .
في الرسم البياني للسرعة كدالة للزمن ، فإن المساحة المحصورة بين الرسم البياني ومحور الزمن تساوي إزاحة الجسم.
نجد إزاحة كل مركبة بمساعدة الرسم البياني، نُشير للسيارة على أنها الجسم 1 ، والدراجة النارية كجسم 2:
نحسب إزاحة السيارة حسب المساحة المحصورة تحت الرسم البياني الذي يصف حركة السيارة:
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نحسب إزاحة الدراجة النارية حسب المساحة المحصورة تحت الرسم البياني الذي يصف حركة الدراجة النارية:
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نجد موقع كل من السيارتين في اللحظة t = 15s:
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إزاحة الدراجة النارية أصغر من إزاحة السيارة ، ولكن بسبب المواقع البدائية في اللحظة t = 15 ثانية ، تسبق الدراجة النارية السيارة.
السؤال يبحث بموقع الأجسام وليس بإزاحتهم ، لذلك من المهم أن نهتم إلى المواقع البدائية كذلك.
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بمرتين.
هذا سؤال منطق. يجب فحص مواقع المركبات في أزمنة مهمة: في لحظة بدء حركتها. في اللحظة t = 5s ، وفي اللحظة t = 15s.
في لحظة بداية الحركة ،تتقدم الدراجة النارية عن السيارة بـ 30 مترًا.
إزاحة السيارة في أول 5 ثوان هي 125 مترا. وإزاحة الدراجة النارية 25 مترا فقط. في اللحظة t = 5s ، تتأخر الدراجة النارية عن السيارة.
في اللحظة ، t = 0s كانت الدراجة النارية متقدمة عن السيارة، وفي اللحظة t = 5s ، أصبحت السيارة تتقدم الدراجة النارية ، لذلك التقيتا بالضرورة مرة واحدة في أول 5 ثوانٍ.
في آخر 10 ثوانٍ ، كانت سرعة السيارة أصغر من سرعة الدراجة النارية ، وكما وجدنا في القسم السابق في اللحظة t = 15 ثانية ، الدراجة النارية تسبق السيارة مرة أخرى.
لذلك ، التقيتا مرة أخرى في آخر 10 ثوانٍ.
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متوسط سرعة الدراجة النارية أصغر من متوسط سرعة السيارة.
زمن حركة الدراجة النارية والسيارة متساويان. لكن الإزاحة مختلفة من تعريف متوسط السرعة فإن متوسط سرعة لكل منهما مختلف.
وجدنا حسب المساحة المحصورة بين الرسم البياني ومحور الزمن ، فإن إزاحة السيارة مساوية 250 مترًا وإزاحة الدراجة النارية 225 مترًا.
زمن الحركة للمركبتين متساوٍ، لذلك من تعريف متوسط السرعة:
لذلك فإن متوسط سرعة الدراجة النارية أصغر.
זמני התנועה זהים , לכן מהגדרת המהירות הממוצעת :
לכן המהירות הממוצעת של האופנוע קטנה יותר.
يكون الموقع النهائي للدراجة النارية أكبر من الموقع النهائي للسيارة ، لكن متوسط سرعة الدراجة النارية أقل من متوسط سرعة السيارة. هذا يعود إلى حقيقة أن الموقع النهائي يتعلق بالموقع الإبتدائي ، لكن متوسط السرعة لا يتعلق بالموقع الإبتدائي.
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باللحظة t=8.33s
من الرسم البياني يمكن ملاحظة أن كلا السيارتين لهما نفس السرعة بالحظة t = 5s ، عندما تتحرك السيارة بتسارع سالب. من الممكن كتابة دالة السرعة كدالة للزمن للدراجة النارية من اللحظة t = 0s ودالة السرعة كدالة للزمن للسيارة من اللحظة t = 5s ، ومقارنة هاتين الدالتين لإيجاد اللحظة التي تكون فيها سرعة الدراجة النارية تساوي سرعة السيارة.
من خلال الرسم البياني يمكن أن نرى أن سرعة السيارتين متساوية عندما تتحرك السيارة بتسارع سالب.
نظرًا لأن التسارع ثابت ، يمكن أن نستخدم دالة السرعة كدالة للزمن لوصف سرعة كل واحدة من المركبتين .
نُشير للدراجة النارية بالجسم رقم 1, نكتب الدالة
الملائمة لوصف حركة الدراجة:
نُشير للسيارة بالجسم رقم 2, نكتب الدالة
الملائمة لوصف حركة السيارة:
نكتب معادلة الأزمنة التي تربط t1 بـ t2. في لحظة الإلتقاء ، يكون زمن تسارع السيارة أقل بخمس ثوانٍ من زمن تسارع الدراجة النارية ، لذلك:
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في اللحظة التي تتساوى فيها سرعة المركبتين يتحقق: V1 =V2. نقارن بين دالتي السرعة:
نحل هيئة المعادلات. ونجد t1 و- t2:
نُعوّض t2 , ونجد t1.
وبالتالي ، فإن سرعت المركبتين تكون متساوية بعد 8.33 ثانية من بدء حركة الدراجة النارية.
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נציב את t2 ,ונמצא את t1.
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לכן מהירויות כלי הרכב זהות כעבור 8.33 שניות מרגע תחילת תנועת האופנוע.
1. يمكن التعامل مع هذا السؤال على أنه سؤال دوال في الرياضيات ، معطى دالتان ويجب إيجاد نقطة تقاطعهما.
2. لا يمكن وصف حركتي المركبتين في دالة واحدة ، المقارنة بين دالة السرعة للزمن للدراجة النارية ودالة السرعة للزمن للسيارة ، والأخذ بعين الإعتبار أن السيارة بدأت حركتها 5 ثوان بعد بدء حركة الدراجة النارية.
2. לא ניתן לתאר את שתי תנועות המכונית בפונקציה אחת, ההשוואה היא בין פונקציית מהירות זמן של האופנוע לפונקציית מהירות זמן של המכונית, ההתייחסות למכונית היא כאל תנועה שהתחילה 5 שניות לאחר תחילת תנועת האופנוע.
2. המכונית נעה בשתי תנועות שונות, ולא ניתן לתאר את שתי התנועות בפונקציה אחת. לכן בתיאור תנועת המכונית , יש לכתוב את פונקציית המהירות בתלות בזמן לתנועה השנייה, בה מהירות המכונית שווה למהירות האופנוע (תנועה שהתחילה 5 שניות לאחר תחילת תנועת האופנוע), והמהירות ההתחלתית בתנועה זו היא המהירות הסופית של התנועה הראשונה.
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