Elastic Collision: In the elastic collision total momentum, the total energy and the total kinetic energy are conserved. However, the total mechanical energy is not converted into any other energy form as the forces involved in the short interaction are conserved in nature. Consider from the above graph two masses, m1 and m2 moving with speed u1 and u2. The speed after the collision of these masses is v1 and v2
m1u1 + m2u2 = m1v1 + m2v2
Inelastic Collision: In the inelastic collision, the objects stick to each other or move in the same direction. The total kinetic energy in this form of collision is not conserved but the total momentum and energy are conserved. During this kind of collision, the energy is transformed into other energy forms like heat and light. Since during the phenomenon the two masses follow the law of conservation of momentum and move in the same direction
m1u1 + m2u2 = (m1+ m2)v