Discuss one-dimensional elastic collision. Obtain an expression for their velocities after collision.

One-dimensional elastic collision is the collision in which the colliding bodies continue to move along the same straight line after collision.
Consider two bodies A and B of masses m₁ and m₂ moving along the same straight line with velocities u₁ and u₂ respectively.

Let the two bodies collide elastically and let and v₂ be the velocities of two bodies after collision. Since collision is elastic collision, therefore, their momentum and kinetic energy remain conserved.
By conservation of momentum,
                
or                                    ...(1)
By conservation of kinetic energy
                   
or                             ...(2)
Dividing (2) by (1), we get,
         
or                                                   ...(3)
Substituting (3) by (1), we get
                           
or                
or                     
or                   
Substituting for  in equation (3), we get