A body moving towards another body of finite mass at rest collides with it. It is possible that:
(i) both bodies come to rest
(ii) both bodies move after collision
(iii) the moving body stops and body at rest start moving
(iv) the stationary body remains stationary and the moving rebounds

$\mathrm{Both} \mathrm{bodies} \mathrm{can} \mathrm{not} \mathrm{come} \mathrm{to} \mathrm{rest} \mathrm{as} \mathrm{it} \mathrm{violates} \mathrm{conservation} \mathrm{of} \mathrm{momentum}$

$$\begin{gathered} \mathrm{both} \mathrm{of} \mathrm{them} \mathrm{starts} \mathrm{moving} \mathrm{is} \mathrm{possible} \mathrm{but} \mathrm{total} \mathrm{momentum} \mathrm{of} \\ \mathrm{the} \mathrm{system} \mathrm{must} \mathrm{be} \mathrm{equal} \mathrm{to} \mathrm{momentum} \mathrm{of} \mathrm{the} \mathrm{colliding} \mathrm{body}. \end{gathered}$$

$\mathrm{for} \mathrm{perfectly} \mathrm{elastic} \mathrm{collision} \mathrm{of} \mathrm{equal} \mathrm{masses} \mathrm{they} \mathrm{exchange} \mathrm{their} \mathrm{velocities}.$

$$\begin{gathered} \text{If stationa}\mathrm{ry} \mathrm{body} \mathrm{rebounds} \mathrm{the} \mathrm{then} \mathrm{the} \mathrm{momentum} \mathrm{by} \mathrm{direction} \\ \mathrm{is} \mathrm{not} \mathrm{conserved} \mathrm{as} \mathrm{the} \mathrm{heavier} \mathrm{body} \mathrm{is} \mathrm{still} \mathrm{at} \mathrm{rest}. \end{gathered}$$