A car starts from rest, then accelerates at a constant rate over a distance of 76 m. It then immediately decelerates at a constant rate over a distance of 123 m. The entire trip lasts a total duration of 21.6 s. What were the magnitudes of the car s accelerations for the speedup and slowdown stages respectively? A0.85 m/s^2, then 0.85 m/s^2 B5.69 m/s^2, then 3.52 m/s^2 C2.23 m/s^2, then 1.38 m/s^2 D3.52 m/s^2, then 5.69 m/s^2

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A car starts from rest, then accelerates at a constant rate over a distance of 76 m. It then immediately decelerates at a constant rate over a distance of 123 m. The entire trip lasts a total duration of 21.6 s. What were the magnitudes of the car s accelerations for the speedup and slowdown stages respectively?

A
0.85 m/s^2, then 0.85 m/s^2

B
5.69 m/s^2, then 3.52 m/s^2

C
2.23 m/s^2, then 1.38 m/s^2

D
3.52 m/s^2, then 5.69 m/s^2

Expert Solution

Step 1

we know that let the initial velocity of the car is u and the car is accelerated with the constant rate of a₁ and travel a distance x₁ in the time t₁ and then immediately car decelerates at a constant rate a₂ and travel a distance x₂ in the time t₂ and stop finallly .

We know that the first equation of motion is given as

$v = u + at$

The third euqtaion of motion is given as

$v^{2} = u^{2} + 2 as$

here s is the distance travel by the car.

Now by useing these two formula we get the answer to this question as

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