Conservation of Momentum

Colliding carts push on each other with equal and opposite forces for the same time, so the total momentum does not change:

m1 v1 + m2 v2 = m1 v1' + m2 v2'

This holds on a smooth track or on ice, where no outside force acts along the motion.

In the picture the total is 11 kg·m/s before and after.

The 2 kg cart catches up, bumps the 3 kg cart and slows down.

A push-off from rest keeps the total at zero: the bodies move apart in opposite directions (recoil).