Question

Derive the relation between kinetic energy and momentum?

Answer 1

Kinetic energy $\left(K\right)=\frac{1}{2}m{v}^2,$ and
Momentum (p) = mv
Where, symbols have usual meaning.
Now,
$K=\frac{1}{2}m{v}^2=\frac{1}{2}m{v}^2\times \frac{m}{m}=\frac{1}{2}\frac{m^2{v}^2}{m}=\frac{(mv{)}^2}{2m}=\frac{p^2}{m}$
therefore,
$K=\frac{p^2}{2m}$