The elastic collision in which the colliding particles moving along the same straight line path before and after the collision is called one-dimensional elastic collision.

Consider two bodies A and B having respective masses m₁ and m₂ are moving with respective velocities u₁ and u₂ is straight line such that u₁ > u₂ before collision as shown in figure . Let, the bodies collide elastically and v₁ and v₂ be their respective velocities after collision.

       Applying law of conservation of linear momentum,

            m₁u_{1 +} m₂u₂ = m₁v₁ +m₂v₂                         ..........(1)

or,       m₁(u₁ – v₁)   = m₂(v₂ – u₂)                          ...........(2)

Since in an elastic collision, total kinetic energy also remains conserved. Therefore,

From equation (7) and (8), the velocities of the bodies A and B, after collision can be calculated.

Special cases

·        When both the colliding are of the equal masses then, m₁ = m₂ = m(say)

From(7), v₁ = u₂

From(8), v₂ = u₁

This shows that if two bodies having equal masses collide elastically in one-dimension, then they simply interchange their velocities after the collision.