A body has a linear momentum of p and a mass of m. The kinetic energy of the…

For a body of mass m moving with speed v, linear momentum is defined as p = mv, and kinetic energy is defined as K = ½mv². These two definitions can be combined by eliminating v, which expresses kinetic energy directly in terms of momentum and mass instead of velocity.

1. From p = mv, write velocity in terms of momentum and mass: v = p/m.

2. Substitute this into K = ½mv²: K = ½m(p/m)².

3. Expand the square and simplify: K = ½m·(p²/m²) = p²/2m.

So the kinetic energy of the body works out to p²/2m.

Cross-check with numbers: take m = 2 kg and v = 3 m/s. Then p = mv = 6 kg·m/s, and directly K = ½mv² = ½ × 2 × 9 = 9 J. Using the derived expression instead, p²/2m = 36/4 = 9 J — the same value, confirming the derivation.