Kinetic energy

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

Émilie du Châtelet (1706–1749) with a pair of compasses in her right hand. She was the first to publish the relation for kinetic energy

E_{\text{kin}}\propto mv^{2}

. This means that an object with twice the speed hits four times – 2×2 – harder. (Portrait by Maurice Quentin de La Tour.)

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]

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.

^ Jain, Mahesh C. (2009). Textbook of Engineering Physics (Part I). p. 9. ISBN 978-81-203-3862-3. Archived from the original on 2020-08-04. Retrieved 2018-06-21., Chapter 1, p. 9 Archived 2020-08-04 at the Wayback Machine
^ Landau, Lev; Lifshitz, Evgeny (15 January 1976). Mechanics (Third ed.). p. 15. ISBN 0-7506-2896-0.
^ Goldstein, Herbert (2002). Classical Mechanics (Third ed.). p. 62-33. ISBN 978-0201657029.

[1] Jain, Mahesh C. (2009). Textbook of Engineering Physics (Part I). p. 9. ISBN 978-81-203-3862-3. Archived from the original on 2020-08-04. Retrieved 2018-06-21., Chapter 1, p. 9 Archived 2020-08-04 at the Wayback Machine

[2] Landau, Lev; Lifshitz, Evgeny (15 January 1976). Mechanics (Third ed.). p. 15. ISBN 0-7506-2896-0.

[3] Goldstein, Herbert (2002). Classical Mechanics (Third ed.). p. 62-33. ISBN 978-0201657029.

[1]

[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, E_k, K or T
SI unit	joule (J)
Derivations from other quantities	E_k = 1/2m v² E_k = E_t + E_r