Momentum is the quantity of motion of a moving mass. A large mass with a certain velocity has a greater momentum than does a small mass with the same velocity. Equal masses moving with equal velocities possess the same quantity of motion. If equal masses have different velocities, then the mass having the greater velocity has the greater momentum. Hence, momentum depends on both the mass of the body and the velocity with which the body is moving. It is measured by the product of the mass and the velocity or: P = mv.
Newton hinted at the quantity called momentum in the original statement of his second law, which reads, "The change of motion is proportional to the impressed motive force and takes place in the direction of the straight line in which the force is impressed." The most important part of the statement is that forces are measured by the change of motion which they produce.
Suppose that two bodies of different mass and different velocities are moving toward each other on a colusion path. When the impact occurs, the brief period during which they are in contact causes them to be deformed. If the bodies are elastic, they will restore the energy it took to deform them by returning to their original shape in a spring-like fashion. From this situation one can deduce that the change of momentum of one of the bodies must be equal to the change of momentum in the other body. Thus, the total momentum of the two bodies has not been changed by the colusion. This leads to the law of conservation of momentum which states that for any colusion, the sum of the momenta of the colliding bodies after colusion must equal the sum of their momenta before colusion.
