Motion itself can carry energy. For a particle of mass $m$ moving with speed $v$, the kinetic energy is

$$K=\frac12mv^2.$$

Kinetic energy is measured in joules and is always nonnegative.

Speed, not velocity direction

Because velocity is squared through its magnitude,

$$K=\frac12m|\mathbf v|^2,$$

two objects with equal mass and equal speed have the same kinetic energy even if they move in opposite directions.

This distinguishes kinetic energy from momentum, which is a vector and changes direction with velocity.

Dependence on mass and speed

Doubling the mass at the same speed doubles the kinetic energy.

Doubling the speed multiplies the kinetic energy by four:

$$\frac12m(2v)^2=4\left(\frac12mv^2\right).$$

The quadratic dependence on speed is important in situations such as braking, impacts and high-speed motion.

Kinetic energy becomes especially useful when changes in motion are related directly to the work done by forces.