The momentum of a particle of mass m is p. Its kinetic energy is:

Concept

For a non-relativistic particle, linear momentum is p = mv, while kinetic energy is K = 1/2 mv2.

Eliminating the velocity between these two definitions expresses kinetic energy in terms of momentum and mass.

Application

1. From p = mv, isolate the velocity: v = p/m.

2. Substitute v = p/m into K = 1/2 mv2.

3. Simplify: K = 1/2 m(p/m)2 = p2/(2m).

Cross-check

The dimensions of p2/m are kg·m2/s2, the dimensions of energy, and the factor 1/2 is retained from the kinetic-energy definition.

Result

Therefore, the kinetic energy is p2/(2m).