Question

Prove that relation between relativistic momentum and kinetic energy is

Answer 1

Sometimes it's desirable to express the kinetic energy of a particle in terms of the momentum. That's easy enough. Since v=p/m and the kinetic energy k=1/2mv^2 so

K=1/2m(p/m)^2 =p^2/2m

Note that if a massive particle and a light particle have the same momentum, the light one will have a lot more kinetic energy. If a light particle and a heavy one have the same velocity, the heavy one has more kinetic energy.

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