posted by Makinin .
Two trains are heading toward each other on the same track with velocities v1 and v2 respectively. The drivers,noticing this when the trains are at distance x apart, apply brakes, giving same acceleration y to each train. The necessary condition for collision is?
[v1*t -(a/2)t^2] + [v2*t - (a/2)t^2] = x
(v1 +v2)*t - a t^2 = x
a is the acceleration rate.
The time t to collision depends upon the deceleration rate a as well as v1+v2 and x.
If there is no real solution to the quadratic, they do not collide.