Kinematics

[xox.happy1.xox]

You add the velocities and acceleration because you want to find out when the rears are just touching each other. I always like to assume that one is stationary, therefore, for them to actually touch rears, the velocities and accelerations need to be added together. I'm sure there is a better explanation

[shinny]

Its because theyre moving in opposite directions. So if you define the direction system so that the positive direction for each separate system (each train basically) as its direction of movement, then you'll end up with two positive accelerations/velocities.

EDIT: typo