The driver of a train moving at a speed ` v_(1)` sights another train at a disane ` d`, ahead of him moving in the same direction with a slower speed ` v_(2)`. He applies the brakes and gives a constant teradation ` a` to his train. Show that here will be no collision if ` d gt (v_(1) -v_(2))^(2) //2 a`.

Explanation

`v_(A//B)=v_(A)-v_(B)=v_(1)-v_(2)`
Now `B` is at rest and `A` is moving with velocity `(v_(1)-v_(2))`.

By the application of brakes, train stops after traveling a distance `s`.
`v^(2)=u^(2)+2as`
`0=(v_(1)-v_(2))^(2)-2a_(0)s`
`s=((v_(1)-v_(2))^(2))/(2a_(0))`
for no collision, `dges`
`dge((v_(1)-v_(2))^(2))/(2a_(0))`
`d_(min)=((v_(1)-v_(2))^(2))/(2a_(0))`