Question

What will be the condition of no collision with the second train?

The drivers of a train moving at a speed `v_1` sight another train at a distance `d` ahead of him on the same line, moving with slower speed `v_2`. 1st driver pulls the brake to create a retardation `r`.

Answer 1

If the driver of first train is able to bring the velocity of his train down from its velocity `v_1` to the velocity `v_2` of train ahead in a distance `d`, the condition for no collision is met.

Using the kinematic expression

`v^2-u^2=2as`
where various symbols have meaning ascribed to them. We get

`v_2^2-v_1^2=2(-r)d`
`=>r=(v_1^2-v_2^2)/(2d)`