# How does acceleration affect momentum?

According to Newton's second law:
If a body is acted upon by a force, the time rate of variation of the body's momentum equals the force.

This sentence seems a bit hostile if not interpreted, so i will try to make it clear.

To get started, let's state this two equations:
$F = m . a \to$ Force equals mass times acceleration
$Q = m . v \to$ Momentum equals mass times velocity

If a body is acted upon by a force,...:
This sentence is our hypothesis, which means this is the given condition of the body.

...the time rate of variation of the body's momentum...:
This sentence requires from us the concept of derivative, but if you have not had a course of calculus yet, do not worry.
Time rate of variation of the momentum is how $Q$ behaves under the effects of time (if it increases or decreases as time passes).

...equals the force.
Let ${Q}_{t}$ be the variation of $Q$ in time:
${Q}_{t} = F \to {Q}_{t} = m . a$
Then, the acceleration times the mass equals the variation of the body's momentum in time.

Example:
A sphere of mass $m = 10 k g$ moves in a gravitational field under a force $F = 50 N$.
If it's velocity at $t = 0 s$ is $0 \frac{m}{s}$, find it's momentum at $t = 10 s$.

Solution:
$Q = {Q}_{0} + t \cdot {Q}_{t} \to {Q}_{0} = 10 k g \cdot 0 \frac{m}{s} \to Q = t \cdot {Q}_{t}$
${Q}_{t} = F \to Q = t \cdot F \to Q = 10 s \cdot 50 N \to Q = 500 N \cdot s$//

Hope it helps.