Question

A purple car is moving three times as fast as a yellow car. Each car slows down to a stop with the same constant acceleration. How much more distance is required for the purple car to stop?
(A) twice as much distance
(B) three times as much distance
(C) five times as much distance
(D) seven times as much distance
(E) nine times as much distance

Answer 1

here there are two cars and one car is moving with a constant speed which is three times the speed of the other car. Thus, both cars have a constant speed. After some time, they slow down and eventually come to halt. Both of them de accelerates at the same rate. We need to find the stopping distance in each case.

Complete step by step answer:
Let the purple car be A and yellow car be B
Let the speed of yellow car be x and as per question speed of purple car= 3x
For car B;
Initial speed, u=x
Final speed, v=0
Acceleration, =-a
Using the third equation of motion

& {{v}^{2}}-{{u}^{2}}=2as \\\ & 0-{{x}^{2}}=-2a{{s}_{B}} \\\ & {{s}_{B}}=\frac{{{x}^{2}}}{2a} \\\ \end{aligned}$$ Now For car A; Initial speed, u=3x Final speed, v=0 Acceleration, =-a Using the third equation of motion $$\begin{aligned} & {{v}^{2}}-{{u}^{2}}=2as \\\ & 0-{{(3x)}^{2}}=-2a{{s}_{A}} \\\ & {{s}_{A}}=\frac{9{{x}^{2}}}{2a} \\\ \end{aligned}$$ That $${{s}_{B}}$$is 9 times $${{s}_{A}}$$. Hence, nine times as much distance more distance is required for the purple car to stop. So, the correct option is (E) **Note:** when a body moves with a constant speed then it has zero acceleration. When the speed of the body increases then its acceleration is positive and when the speed of the body decreases then acceleration is negative.