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 

Asked by Sayoni Maiti | 4th Jun, 2014, 10:39: AM

Expert Answer:

For no collision the velocity of A must reduce to that of velocity of B.
VA = 30 m/s , VB = 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 ( VA-VB )
The relative acceleration of A with respect to B is (-a - 0 ) = - a
Using the equation : v2= u2+ 2as
0 = ( VA-VB )2 + 2 × -a × s'
s' = ( VA-VB )2 / 2 a
= (30-20) 2 / 4
=25 m
Hence no collision occurs when d is greater than 25 m

Answered by Jyothi Nair | 4th Jun, 2014, 04:56: PM