A car moving at a speed u is stopped in a certain distance when the brakes produce a deceleration a. If the speed of the car is nu, what must be the deceleration of the car to stop it in the same distance?
n2a
From the third equation of motion, v2=u2−2as
⇒0=u2−2as
⇒s=u22a
So, the distance over which the car is stopped is given by s=u22a.
If initial velocity is nu, let the value deceleration to stop the car in the same distance be a′.
02=(nu)2−2a′s⇒0=n2u2−2a′(u22a)⇒a′=n2a
Hence, the correct choice is (c).