## Kinetic energy

Glossary Definition for 16-19

#### Description

Kinetic energy is energy associated with motion.

Kinetic energy is usually represented by the symbol *E*_{K} or the abbreviation KE.

In Newtonian physics, the kinetic energy of an object of mass m, travelling at speed v, is defined by the equation:

*E*_{K} = 12*m**v*^{ 2}

#### Discussion

Kinetic energy is not an absolute quantity because to measure the speed of an object, there must be an observer with respect to whom the object is (or is not) moving. The expression for an object’s kinetic energy, 12*m**v*^{ 2}, is accurate in classical, Newtonian physics for speeds much less than the speed of light.
At very high speeds, the expression for the kinetic energy is modified to become

*E*_{K} = (γ-1)*m*_{0}*c*^{ 2}

where *m*_{0} is the mass of the particle measured when it is at rest, *c* is the speed of light and

γ = *1* *1-( v^{ 2}/c^{ 2})*

In the limit

*v*<<

*c*, this expression for

*E*

_{K}reduces to the classical 12

*m*

*v*

^{ 2}.

#### SI unit

joule, J

#### Expressed in SI base units

kg m^{2} s^{-2}

#### Mathematical expressions

*E*_{K}= 12*m**v*^{ 2}

is the kinetic energy of an object with mass*m*moving at speed*v*.

#### Related entries

- Energy of a system
- Internal energy
- Potential energy

#### In context

The typical kinetic energies of the following objects are of the orders of magnitude indicated:

A runner of mass 70 kg running at about 5 m s^{-1}: 10^{3} J.

A car of mass 2000 kg travelling at 70 mph (about 31 m s^{-1}) on a motorway: 10^{6} J.

An electron moving randomly in a metal at room temperature: 10^{-19} J.