Kinetic energy

Kinetic energy
The cars of a roller coaster reach their maximum kinetic energy when at the bottom of the path. When they start rising, the kinetic energy begins to be converted to gravitational potential energy. The sum of kinetic and potential energy in the system remains constant, ignoring losses to friction.
Common symbols	KE, Ek, K or T
SI unit	joule (J)
Derivations from other quantities	Ek = ⁠1/2⁠mv2 Ek = Et + Er

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Classical mechanics
${\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}$ Second law of motion
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Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Koopman–von Neumann mechanics
Core topics Damping Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational frequency Angular acceleration / displacement / frequency / velocity
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In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.^[1]

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is ${\textstyle {\frac {1}{2}}mv^{2}}$.^[2]

The kinetic energy of an object is equal to the work, force (F) times displacement (s), needed to achieve its stated velocity. Having gained this energy during its acceleration, the mass maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest.^[2]

The SI unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound.

In relativistic mechanics, ${\textstyle {\frac {1}{2}}mv^{2}}$ is a good approximation of kinetic energy only when v is much less than the speed of light.