The formula for an elastic collision for the conservation of momentum is m1v1 + m2v2 = m1v1 + m2v2. The formula for the conservation of kinetic energy in an elastic collision is 1/2 m1v1^2 + 1/2 m2v2^2 = 1/2 m1v1^2 + 1/2m2v2^2.
A collision is considered elastic whenever the two colliding objects bounce off of each other. During elastic collisions, the kinetic energy and the momentum are conserved. For this reason, two equations must be used to describe what occurs during an elastic collision. Other types of collisions include inelastic collisions and completely inelastic collisions. During both types of inelastic collisions, kinetic energy is not conserved. Collisions are considered inelastic when the two colliding objects stick to each other and move together.