What is a perfect inelastic collision ? Derive the expression of the common velocity after collision.

Explanation

(i) In a perfectly inelastic or completely inelastic collision, the objects stick together permanently after collision such that they move with common velocity.
(ii) Let the two bodies with masses `m_(1)` and `m_(2)` move with initial velocities `u_(1)` and `u_(2)` respectively before collision.
(iii) After perfect inelastic collision both the object move together with a common velocity v as shown in Figure.
(iv) Since, the linear momentum is conserved during collisions,
`m_(1)u_(1)+m_(2)u_(2)=(m_(1)+m_(2))v`

Perfect inelastic collision in one dimension
The common velocity can be computend by
`v=(m_(1)u_(1)+m_(2)u_(2))/((m_(1)+m_(2)))`