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

Answer: (E)

Nine times as much distance

Let $u$ represents the initial velocity of the car and $a$ be its acceleration.

Final velocity of the car is zero i.e $v=0$ $m/s$

Using $v^2-u^2=2aS$

$\therefore$ $0-u^2=2aS$ $⟹|S|=\frac{u^2}{2|a|}$

Given : $u_p=3u_y$ $a_p=a_y=a$

$⟹$ $\frac{S_p}{S_y}=\frac{u_p^2}{u_y^2}$

OR $\frac{S_p}{S_y}=\frac{9u_y^2}{u_y^2}=9$ $⟹S_p=9S_y$

Thus purple car requires 9 times as much as distance required by yellow car.