A train is moving at a constant speed `V` when its driver observes another train in front of him on the same track and going in the same direction with constant speed `v`. If the distance between the trains is `x` then what should be the minimum retardation of the train so as to avoid collision?.

Options

A. ` (v + v_1^2) d`
B. (v -v_1)^2` d`
C. (v +v_1 )^(1//2)d`
D. (v -v_1 ^(2//2)d`

Answer

D

Explanation

Relative velocity of a train with respect to another
train, ` u= (v-v_1)`
using , ` v^2 - u^2 = aS`, we have
` 0- (v-v_1)^2 = 2 a xx d`
or ` a= - ((v-v_1)^2)/(2d)`.