Consider the collinear motion of two spheres of masses m₁ and m₂ travelling with velocities V₁and V₂ . If V₁ > V₂ , collision occurs with the contact forces directed along the line of centers. This condition is called direct central impact. Following initial contact, a short period of increasing deformation takes palce until the contact area between the spheres ceases to increase. At this instant, both the spheres are moving with the same velocity V₀ . During the remainder of contact, a period of restoration occurs during which the contact area decreases to zero. In this period, mass m₂ is applying a force on m₁ opposite to motion. Hence, the velocity of m₁ keeps on decreasing till the spheres separate out. Because of Newton's third law, the particle m₁ aplies a force on m₂ along the direction of motion. Hence the velocity of m₂ keeps on increasing. Thus, after the impact velocity of m₁ will always be lower than the velocit y of m₂.

In the elastic impact, the original shapes of the bodies are restored. In the inelastic impact, the shapes of bodies are not restored. In the perfectly plastic impact, bodies remain in contact and do not separate out.

Applying the law of conservative of linear momentum

       

The above equation contains two unknown to be determined and . Thus one more equation is needed to solve the impact problem. For this purpose , the coefficient of restitution is defined. The coefficient of restitution e is the ratio of the magnitude of the restitution impulses to the magnitude of the deformation impulses.