The kinetic energy of a particle having mass m is E. Its momentum will be:

Concept

In non-relativistic mechanics, kinetic energy is E = (1/2)mv2, while momentum is p = mv.

Eliminating velocity gives E = p2/(2m); the magnitude of momentum is non-negative.

Application

1. Let p denote the magnitude of momentum. Start with E = p2/(2m).

2. Multiply both sides by 2m: p2 = 2mE.

3. Take the non-negative square root: p = √(2mE).

Cross-check

Substituting p = √(2mE) into p2/(2m) gives (2mE)/(2m) = E, which reproduces the given kinetic energy.

Therefore, the magnitude of momentum is √(2mE).