# Question #f209e

Dec 1, 2017

Force is rate of change of momentum.

#### Explanation:

Force can change the velocity of any object. That means it can change the direction and/or speed of the object.

When there is change in velocity with respect to time, we call it acceleration '$a$'.

$a = \frac{{v}_{2} - {v}_{1}}{t}$ ---- where ${v}_{1}$ is initial velocity and ${v}_{2}$ is final velocity.
and

$F = m a$--------where $m$= mass of the object.

$\implies F = m \left(\frac{{v}_{2} - {v}_{1}}{t}\right)$

$\implies F = \frac{m {v}_{2} - m {v}_{1}}{t}$----using distributive property.

We know $m v = p$ is momentum.

$\implies F = \frac{{p}_{2} - {p}_{1}}{t}$ ---Where ${p}_{2}$ is final momentum and ${p}_{1}$ is initial momentum.

That means force is rate of change of momentum.