A driver of an express train moving with a velocity v1 finds that a goods train is moving with velocity v2 in the same direction on the same track. He applies the brakes and produces a retardation a' the minimum time required to avoid collision is
Relative velocity of express train with respect to goods train
u=v1-v2
If the collision is to be avoided, the relative final velocity v should be zero. Let f is the time required. Then