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 ?

Explanation

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.