Law of conservation of momentum

The Law of Conservation of Momentum states that "If a group of bodies are exerting forces on each other, their total momentum remains the same before and after the interaction provided there is no external forces acting on them.

For example:
Two bodies A and B of masses m₁ and m₂ are moving in the same direction with initial velocities u₁ and u₂ . Suppose they collide each other. Let us assume that they continue moving in the same direction after collision.If the collision last for a very short interval of time 't' seconds.
During collision, A exerts a force on B. At the same time, B exerts a force on A. Due to these action and reaction forces the velocities of A and B get changed. After collision, let v₁ and v₂ be the velocities of the bodies A and B respectively.

i.e, m1v1-m1u1=-m2v2-m2u2