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A 0.145 kg baseball flies past at 40 m/s; a 45 kg child jogs by at 3 m/s. The ball moves 13× faster — so it must be harder to stop. Which one would actually flatten you?
A 0.145 kg baseball flies past at 40 m/s; a 45 kg child jogs by at 3 m/s. The ball moves 13× faster — so it must be harder to stop. Which one would actually flatten you?
Speed alone is a trap: what makes something hard to stop is mass and speed together — momentum, p = mv. The ball carries 5.8 kg·m/s; the child carries 135 — about 23× more. To change that momentum you need a force acting over time, and that single idea explains airbags, crumple zones, and bending your knees on landing.
Momentum p = mv measures 'quantity of motion' — why a slow lorry is harder to stop than a fast bicycle. To change momentum you apply a force over time, and that product is the impulse . The impulse–momentum theorem says impulse equals the change in momentum: . Rearranged as , it tells you that stretching the contact time shrinks the force.
Impulse equals momentum change because Newton's second law, F = ma = m(Δv/Δt), times Δt gives . Same law, accumulated over time. This is why airbags, crumple zones, and bending your knees all work: Δp is fixed, so stretching Δt shrinks the peak force F by the same factor. A cyclist hitting a wall in 0.003 s feels 260 000 N — fatal; the same Δp over 3 s of cushioned stopping is 260 N — survivable. Same momentum change, 1000× less force. Crumple zones don't make the crash gentler by absorbing 'extra' impulse — they simply buy time.
Judging a collision by the peak force alone — what changes momentum is impulse = force × time, so a small force over a long time can match a big force over a short time.