3.3.2—The principle of conservation of momentum to solve simple problems

In one dimension, write m₁u₁+m₂u₂=m₁v₁+m₂v₂, with velocities signed along one chosen axis.

List known masses and velocities, keep units consistent, then solve for the unknown. A negative result means motion opposite to the chosen positive direction.

A 2 kg cart at 3 m s⁻¹ sticks to a 1 kg cart at rest: 6=(3)v, so the joined speed is 2 m s⁻¹ in the original direction.

Do not replace momentum with speed, and do not drop the sign of a cart moving in the opposite direction.