### Freight Train

The engineer of a train which is moving at a speed $v_{1}$ sees a freight train on the same track, at a distance d ahead of him.
The freight train is moving in the same direction, but with a slower speed $v_{2}$. He puts on the brakes and gives his train a constant deceleration $a$.
Show that:
If $d>\frac{(v_{1}-v_{2})^{2}}{2a}$ , there will be no collision.
If $d<\frac{(v_{1}-v_{2})^{2}}{2a}$ , there will be a collision.
(It is a good idea to plot a qualitative graph of x versus t for each train.)