Two bodies of mass $m_1 = 3$ kg and $m_2 = 2$ kg move towards each other with speeds $v_1 = 4$ m/s and $v_2 = 6$ m/s. The collision is perfectly inelastic. Find the speed and direction of motion of the bodies after the collision.
Take the direction of motion of the first body as positive. The momentum of the system before the collision (the bodies move towards each other, so the sign is negative):
$$p = m_1 v_1 - m_2 v_2 = 3 \cdot 4 - 2 \cdot 6 = 12 - 12 = 0$$
After a perfectly inelastic collision the bodies move together:
$$p = (m_1 + m_2) v \Rightarrow 0 = 5v \Rightarrow v = 0$$
The bodies come to a complete stop.
$v = 0$ — the bodies stop after the collision