where                                                                      (6)

Combining equations (5) and (6) ;                              (7)

Equations and may be combined to form the equalities:

          (8)

Equation (8) contains the well-known expression MD V = mD v, registering the inverse relationship between mass and velocity change in a collision. MD V = mD v can also be expanded into the expression for the Conservation of Momentum:

                                                                    (9)

From experimentation and observation it has been noted that colliding bodies generally move apart at the conclusion of an impact. Let the approach velocity and departing velocity between the two bodies be denoted by v_c and v_d respectively, so that:

                                                                                  (10)

Note that v₂ > V₂ in order that the bodies move apart. This rebound is called the Coefficient of Restitution, and let us designate it by the symbol, e .

Therefore:                                                                 (11)

In practice e varies from zero, where there is no rebound, to unity, where there is a full rebound. Zero rebound is usually referred to as a perfectly plastic collision and full rebound is deemed to be a perfectly elastic collision. Equations (4),(7) and (11) may be combined to produce the impulse expression, [Duff, 1998]:

                                                              (12)

from which the equalities of statement may be expanded to:

(13)