How momentum and collisions work
Momentum is mass times velocity:
p = m × v
Its usefulness is the conservation of momentum: in any collision or explosion with no significant external force, the total momentum of the system is the same before and after. Momentum is a vector, so direction matters — a 2 kg object at +3 m/s and a 5 kg object at rest carry a total of 6 kg·m/s, and if they stick together they move at 6 ÷ 7 ≈ 0.857 m/s, in the original direction of the first object.
Worked example
A 2 kg trolley rolling at 3 m/s hits a stationary 5 kg trolley and they stick together. Before: p₁ = 6, p₂ = 0, total 6 kg·m/s. After: (2 + 5)v = 6, so v ≈ 0.857 m/s — together they move slowly in the first trolley's direction. The same total momentum is shared across more mass, which is why combining masses always slows the combined object down. In the everyday version: a bullet fired into a block of clay leaves the pair moving at a crawl, while a moving car hitting a stationary one is pushed only slightly slower.
Momentum, energy and impulse — how they differ
Momentum and kinetic energy are not the same thing, and a collision can conserve one without conserving the other. A perfectly elastic collision (a good billiards-ball break) conserves both momentum and kinetic energy. A perfectly inelastic collision (the trolleys sticking) conserves only momentum — the lost kinetic energy turns into heat, sound and deformation. Momentum's other key role is impulse: the change in momentum equals the average force times the contact time, which is exactly why a cricket pad works — it doubles the stopping time and so halves the peak force on your bones.