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
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
the trains will not collide.