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:

$$\relax m_{1} v_{1} + m_{2} v_{2} = m_{1} v_{1}' + m_{2} v_{2}'$$

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

In the picture the total is $11\ \mathrm{kg\cdot m/s}$ before and after.

The $2\ \mathrm{kg}$ cart catches up, bumps the $3\ \mathrm{kg}$ cart and slows down.

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