Grade 12 Physics · Energy of motion
Why the square matters more than anything
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Why the square matters more than anything

A moving mass carries energy, and the amount is Ek=12mv2E_k = \tfrac{1}{2} m v^{2} — read aloud, E-k equals one-half m v squared. The subscript k is for kinetic. EkE_k is the kinetic energy in joules, mm is the mass in kilograms, and vv is the speed in metres per second. Solve it for whichever letter the question withholds.

Two features, both non-negotiable. The ½ is exact — it falls out of adding up mama over the distance, and a force that grows from zero does, on average, half its maximum. The square is where the danger lives: double the speed and the energy goes up four times. That is not a curiosity, it is the reason a car at 100 km/h needs roughly four times the stopping distance of the same car at 50 — the brakes have four times as many joules to remove, and they remove them at much the same rate per metre.

Keep it separate from its lookalike. Momentum p=mvp = mv uses the same two ingredients and comes out in kg·m/s; kinetic energy squares the speed, halves the product, and comes out in joules. Same pantry, different dish — and the units will tell you which one you cooked.