# What is the relation between kinetic energy and momentum ?

Jul 2, 2016

$P = \sqrt{2 m E}$

#### Explanation:

$P : \text{momentum of object}$
$E : \text{The kinetic energy of object}$
$m : \text{mass of object}$
$v : \text{velocity of object}$

$\text{momentum is expressed as } P = m \cdot v$

${P}^{2} = {m}^{2} \cdot {v}^{2}$

${P}^{2} / m = m \cdot {v}^{2}$

$\textcolor{red}{\frac{1}{2}} \cdot {p}^{2} / m = \textcolor{red}{\frac{1}{2}} \cdot m \cdot {v}^{2}$

$\text{The kinetic energy of an object is written a s } E = \frac{1}{2} \cdot m \cdot {v}^{2}$

${P}^{2} / \left(2 \cdot m\right) = E$

${P}^{2} = 2 \cdot m \cdot E$

$P = \sqrt{2 m E}$