Kinetic energy

In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.[1] It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time and the second term in a Taylor expansion of a particle's relativistic energy. [2][3]

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

Part of a series on
Classical mechanics
${\displaystyle {\textbf {F}}={\frac {\mathrm {d} }{\mathrm {d} t}}(m{\textbf {v}})}$ Second law of motion
History Timeline Textbooks
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical
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 ratio Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion 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
Scientists Kepler Galileo Huygens Newton Horrocks Halley Maupertuis Daniel Bernoulli Johann Bernoulli Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Cauchy Routh Liouville Appell Gibbs Koopman von Neumann
Physics portal  Category
v t e

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is ${\textstyle {\frac {1}{2}}mv^{2}}$. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light.

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