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Problem I am playing with rolling car and give it an initial velocity of vo. I determine that the acceleration of the car is a linear variation from ao to an. After t1, the acceleration stays at an1-2 until t2. I clocked the velocity of the car at t; to be va. Please calculate a) what t; was since I forgot to write it down, and b) how fast the car was going at t2, and c) how far from the start the car was at t2. Givens: Vo = 6 m/s ao = -12 m/s? an = -2 m/s² an-42 = -2 m/s2 t2 = 1.4 s -12 V1 = 1.8 m/s

Problem I am playing with rolling car and give it an initial velocity of vo. I determine that the acceleration of the car is a linear variation from ao to an. After t1, the acceleration stays at an1-2 until t2. I clocked the velocity of the car at t; to be va. Please calculate a) what t; was since I forgot to write it down, and b) how fast the car was going at t2, and c) how far from the start the car was at t2. Givens: Vo = 6 m/s ao = -12 m/s? an = -2 m/s² an-42 = -2 m/s2 t2 = 1.4 s -12 V1 = 1.8 m/s

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem I am playing with rolling car and give it an initial velocity of vo. I determine that the acceleration of the car is a linear variation from ao to an. After tı, the acceleration stays at a1-2 until t2. I clocked the velocity of the car at t to be va. Please calculate a) what t; was since I forgot to write it down, and b) how fast the car was going at t2, and c) how far from the start the car was at t2. t2 Givens: Vo = 6 m/s ao = -12 m/s? an = -2 m/s? an-2 = -2 m/s? tz = 1.4 s Vu = 1.8 m/s -12 Steps to Solve: 1) First, using the provided acceleration equation above for 0<t<ti, derive an equation for velocity during that time period (hint: acceleration is the time derivative of velocity). Be sure you derive the equation in terms of t – you'll use this later. 2) Once you have the equation for velocity, plug in the given velocity (va) to find t1. This is the first variable you were asked for. 3) Now find the position of the car at tı. You'll do this by using the equation you created in Step 1 to derive an equation that relates position to time (hint: velocity is the time derivative of position). 4) Next, you'll want an equation for velocity during the interval ti<t<t2. a) You can do this in different ways (one way is knowing that acceleration is the time derivative of velocity, the other way is recognizing that the acceleration during this time period is constant). b) The result will be the second value you were asked to calculate (how fast the car was going at t2. 5) Lastly, you'll need to create an equation for the position of the car at t2. a)Again you can do this in one of two ways like Step 4. You can remember that the acceleration during this time is constant or you can recall that velocity is the time derivative of position. b) This should give you the third and final answer for the problem (how far from the start you are).
Transcribed Image Text:Problem I am playing with rolling car and give it an initial velocity of vo. I determine that the acceleration of the car is a linear variation from ao to an. After tı, the acceleration stays at a1-2 until t2. I clocked the velocity of the car at t to be va. Please calculate a) what t; was since I forgot to write it down, and b) how fast the car was going at t2, and c) how far from the start the car was at t2. t2 Givens: Vo = 6 m/s ao = -12 m/s? an = -2 m/s? an-2 = -2 m/s? tz = 1.4 s Vu = 1.8 m/s -12 Steps to Solve: 1) First, using the provided acceleration equation above for 0<t<ti, derive an equation for velocity during that time period (hint: acceleration is the time derivative of velocity). Be sure you derive the equation in terms of t – you'll use this later. 2) Once you have the equation for velocity, plug in the given velocity (va) to find t1. This is the first variable you were asked for. 3) Now find the position of the car at tı. You'll do this by using the equation you created in Step 1 to derive an equation that relates position to time (hint: velocity is the time derivative of position). 4) Next, you'll want an equation for velocity during the interval ti<t<t2. a) You can do this in different ways (one way is knowing that acceleration is the time derivative of velocity, the other way is recognizing that the acceleration during this time period is constant). b) The result will be the second value you were asked to calculate (how fast the car was going at t2. 5) Lastly, you'll need to create an equation for the position of the car at t2. a)Again you can do this in one of two ways like Step 4. You can remember that the acceleration during this time is constant or you can recall that velocity is the time derivative of position. b) This should give you the third and final answer for the problem (how far from the start you are).
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