Derive a relationship between kinetic energy and linear momentum.

Step 1: We know that,

Kinetic energy$=\frac{1}{2}m{v}^2$ ……..1

Linear momentum $=m\times v$……..2

Where $m$ is mass and $v$ is velocity

Step 2:

From equation 1

$K.E=\frac{1}{2}m{v}^2$

Multiplying equation by $\frac{m}{m}$

$K.E\times m=\frac{1}{2}{m}^2{v}^2$

From the equation$2$, we know that $mv=p$ (linear momentum)

On putting $P$ in place of $mv$

$K.E\times m=\frac{1}{2}{P}^2$

$$\begin{gathered} P^2=2\times m\times K.E \\ P=\sqrt{2mK.E} \end{gathered}$$

Above is the relationship between the kinetic energy of a body and its linear momentum.