Question

A car moving at a speed $v$ is stopped in a certain distance when the brakes produce a deceleration $a$ . If the speed of the car was $nv$ , what must be the deceleration of the car to stop it in the same distance and in the same time?

• A. $\sqrt{na}$
• B. $na$
• C. $n^{2}a$
• D. $n^{3}a$

Answer 1

The correct option is C $n^{2}a$

The deceleration of the car is given as,

$a=\frac{v^2}{2s}$

If the speed of the car was $nv$ then the new deceleration is given as,

$a^{\prime }=\frac{{\left(nv\right)}^2}{2s}$

$=\frac{n^2{v}^2}{2s}$

$=n^{2}a$

Thus, the new deceleration of the car is $n^{2}a$.