How is it possible that two moving objects can collide and stop moving?

Answer 1

This can happen if they move in opposite directions, and the sum of their momentum is zero. For example, before the collision one may have a momentum of 100 kg x meter / second to the right, and the other 100 kg x meter / second to the left. Thus, their total momentum before the collision would be zero; therefore this would be no problem from this point of view, since the total momentum after the collision is obviously also zero.

From the point of view of conservation of energy, mechanical energy is often lost in collisions; most of such energy is converted into heat energy.

Answer 2

When two objects collide, they exert forces on each other that can change their motion. These forces can slow down the objects and eventually bring them to a stop if enough energy is transferred during the collision. This transfer of kinetic energy can cause the objects to stop moving after the collision.