Kinetic Energy (J)

Kinetic energy: Ec = (1/2)·m·v²

Kinetic energy is what a body carries simply by moving: Ec = (1/2)·m·v², measured in joules, with mass in kg and velocity in m/s. Notice that it is quadratic in v, so double the speed and the energy goes up four times. A 1,500 kg car at 100 km/h (27.8 m/s) carries about Ec ≈ 579 kJ; a 9 mm bullet weighing 8 g at 350 m/s holds 490 J. The work-energy theorem ties this together: the net work done on a body equals its change in kinetic energy, W = ΔEc. Braking distance obeys d = v²/(2·μ·g), which also scales with the square of the speed.

Applications

You see it in vehicle crash tests (kJ at 50/60 km/h), in highway braking distances, in forensic ballistics, on roller coasters, and in free fall, where Ec climbs as Ep drops. Wind turbines are a striking case: the wind's kinetic energy follows (1/2)·ρ·A·v³, which is cubic in wind speed, so even a small gain in wind speed pays off as a big gain in power.

FAQ

Why does doubling speed quadruple the energy? Because velocity shows up squared in the formula. Move from 50 to 100 km/h and the crash energy goes up by four, not by two.

Is kinetic energy a vector? No. It is a scalar and never goes below zero, which sets it apart from momentum p = m·v, a vector quantity.

How does Ec relate to potential energy? Whenever a system is conservative and frictionless, mechanical energy stays constant: Ec + Ep = constant. Watch a ball drop and you see Ep turning into Ec.