Two cars A and B are moving  in same direction with velocities 30 m/s and 20 m/s respectively.when car A is at a distance d behind the car B, the driver of car A applies brakes producing uniform retardation of 2 m/s square . there will be no collision when -

 

        a)d is lesser than 2.5 m

        b)d is greater than 125 m

        c)d is greater than 25 m

        d)d is lesser than 125 m 

For no collision the velocity of A must reduce to that of velocity of B.

V_A = 30 m/s , V_B = 20 m/s , a = - 2 m/s²

i.e. the relavitive final velocity of A with respect to B must be 0. Vr = 0

The relative initial velocity of A with respect to B is ( V_A-V_B )

The relative acceleration of A with respect to B is (-a - 0 ) = - a

Using the equation : v²= u²+ 2as

0 = ( V_A-V_B )² + 2 × -a × s^'

s^' = ( V_A-V_B )² / 2 a

= (30-20) ² / 4

=25 m

Hence no collision occurs when d is greater than 25 m