Momentum and its conservation
Momentum is mass times velocity, and in any collision the total stays the same. One equation, "momentum before momentum after", solves the whole topic.
≈ 30 minDirections, rebounds and several collisions
Head-on collisions and rebounds are where signs matter. Fix a positive direction, give every velocity a sign, and let the algebra tell you which way things end up moving.
≈ 35 minCoalescing and loss of kinetic energy
When particles stick together they share one velocity, so conservation of momentum gives it directly. Momentum survives the crash; kinetic energy does not, and the difference has gone into heat, sound and crumpled metal.
≈ 30 min