The Driver Of A Train Moving At A Speed at V1, sights another train at a distance d, ahead of him moving in the same direction with a slower speed V2. He Applies The Brakes And Gives A Constant retardation a to his train. Show That there will be no collision If d>(V1-V2)*2/2a.
For the train A,
Initial velocity = v1
Retardation = a
Distance it has to travel to avoid collision is = d
For train B,
Velocity of travel = v2
The relative velocity of A with respect to B is, u = v1 – v2.
The relative velocity becomes zero for the trains to avoid collision. That is, final relative velocity is, v = 0 [at this moment the trains have equal velocity]
Now, using, v2 = u2 – 2as [negative sign appears since a is retardation]
=> 0 = (v1 – v2)2 – 2ad
=> d = (v1 – v2)2/(2d)