Question

Derive relation between Linear momentum and kinetic energy.

Answer 1

Sometimes it's describe to express the kinetic energy of a particl in terms of the momentum That's easy enough$.$ Since $v=p/m$ and the kinetic energy $K=\frac{1}{2}m{v}^2$

$K=\frac{1}{2}m{\left(\frac{p}{m}\right)}^2=\frac{p^2}{2m}$

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$.$