Whenever two objects are in contact, they exert equal and opposite forces on each other.

Whether they are in contact for a measurable time, or just for a split second, it is char that each is in contact with the other for the same time. Therefore they exert equal and opposite impulses on each other.

Provided that neither object is fixed, these equal and opposite impulse produce equal and opposite changes in momentum, so the overall change in momentum of the two objects caused by the collision is zero. Hence, so long as no external farce acts on either object, the total momentum of the two objects (which we refer to as the system) remains constant.

This property is known as The Principle of Conservation of Linear Momentum and is expressed formally as follows:

If in a specified direction, no external force affects the motion of a system, the total momentum in that direction remains constant.

In some problems involving a collision the two colliding objects bounce and so have individual velocities after impact. Other objects collide and join together at impact, e.g. trucks which become coupled. Such objects are said to coalesce.

In either case we are dealing with different velocities before and after impact so it is advisable to draw separate `before' and `after' diagrams and to define the chosen positive direction particularly carefully.