Definition

Kinetic energy is the energy something has because it is moving; faster objects and heavier objects have more of it. It is given by $KE = \tfrac{1}{2}mv^2$, where $m$ is mass in kilograms and $v$ is speed in meters per second, with the joule as its unit, and because speed is squared, kinetic energy grows quickly as objects speed up and is never negative. In full, $K = \tfrac{1}{2}mv^2 = p^2/2m$, a scalar derived from the work-energy theorem: the net work done on a particle equals its change in kinetic energy, $W_{\text{net}} = \Delta K$. For extended bodies, total kinetic energy splits into translational motion of the center of mass plus rotational energy $\tfrac{1}{2}I\omega^2$. The classical formula is the low-speed limit of the relativistic expression $K = (\gamma - 1)mc^2$.