MOMENTUM & ENERGY

The CM worldline runs straight through the wreck — that line IS momentum.

Δp = 0 while 98.7% of the KE dies — measure a bullet with a protractor.

Δv = vₑ·ln(m₀/m) — every m/s borrowed from the exhaust, and the ln collects.

Loop-the-loop by the energy ledger — clear it only if released from h ≥ 2.5r, mass be damned.

Braking distance grows as v² — double your speed, quadruple the road; the v² law, priced.

½kx² becomes ½mv² becomes mgH — one joule in three costumes, and it is shm’s peak speed.

Impulse is force × time, and it equals the change in momentum: J = FΔt = Δp. Stretch the contact time and the force drops in step — the physics of every airbag.