Kinetic Energy (J)
Calculates kinetic energy in joules given mass in kg and velocity in m/s via 0.5·m·v².
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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.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.