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 ->` Force equals mass times acceleration
`Q = m.v ->` 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 -> 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 = 10kg` moves in a gravitational field under a force `F = 50N`.
If it's velocity at `t = 0s` is `0m/s`, find it's momentum at `t=10s`.

Solution:
`Q = Q_0+t*Q_t -> Q_0 = 10kg * 0m/s -> Q = t*Q_t`
`Q_t = F -> Q = t*F -> Q = 10s*50N -> Q = 500N*s`//

Hope it helps.