A collision is called elastic if kinetic energy is also conserved along with the linear momentum. There is no transformation or loss of kinetic energy in this collision

Suppose two particles of masses m₁ and m₂ moving with velocities  and  respectively. They interact and their velocities after the collision become  and  respectively.

By conservation of the linear momentum,

 and only for linear collision or head on collision 

On solving the above equation (1) and (2),                ... (3)           

i. e. Relative velocity before collision = Relative velocity after collision.

Thus in elastic collision, the relative velocity of tends to of particles before collision is same to the relative velocity with which the particles recedes after collision. i.e. the  value of relative velocity keeps the same, but the direction is reversed.

On solving the equation (1) and (3) we get

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