A collision is said to be elastic if the total kinetic energy before and after collision remain the same or KE is conserved. Thus, if two bodies of masses m1 and m2 moving with velocities u1 and u2 collide in absence of external force also elastically and v1 and v2 are the final velocities, then according to conservation of momentum m1u1+m2u2=m1v1+m2v2 Also, according to principle of conservation of KE 21mu12+21mu22=21mv12+21mv22 Therefore, it is clear that both kinetic energy and momentum are conserved.