A driver of train A, moving at a speed 30 ms^(-1), sights another train B going on the same track and in the same direction with speed 10 ms^(-1). He immediately applies brake that gives his train a constant retardation of 2 ms^(-2). What must be the minimum distance between trains in order to avoid a collision ?

A driver of train A, moving at a speed 30 ms^(-1), sights another trai

1.	A driver of train A, moving at a speed 30 ms^(-1), sights another train B going on the same track and in the same direction with speed 10 ms^(-1). He immediately applies brake that gives his train a constant retardation of 2 ms^(-2). What must be the minimum distance between trains in order to avoid a collision ?
Answer» Solution :The initial velocity of the train, `v_(0) = v_(AB) = v _(A) -v _(B) = 30 - 10 = 20 ms ^(-1)` Now `v ^(2) -v _(0) ^(2) = 2ax,` here, `v =0, v _(0) = 20 , a =- 2MS ^(-2)` `therefore (0) ^(2) - (20) ^(2) = 2 (-2) x` `therefore (-400)/(-4) =x` `therefore x = 100 m` ACCIDENT can be avoided if the minimum DISTANCE 100 m is kept between two trains.