### Freight Train

The engineer of a train moving at a speed

sights a freight
train a distance d ahead of him on the same track, moving in the same
direction with a slower speed

He puts on the brakes and
gives his train a constant deceleration

Show that:

At the first moment, the relative speed between the two trains is

If the two trains reach a relative speed of 0 they will crash.

We need the formula:

This formula is in your book, but you can also get it by taking

and plugging it into the formula

In our case we take the relative speed between them as v(t), and

and if

the trains will not collide.