How does acceleration affect momentum?

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How does acceleration affect momentum?

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Answer 1 · 2014-10-04T01:38:24

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:
$F = m . a \to$ $F = m.a ->$ Force equals mass times acceleration
$Q = m . v \to$ $Q = m.v ->$ 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 $Q$ $Q$ behaves under the effects of time (if it increases or decreases as time passes).

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

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

Solution:
$Q = Q_{0} + t \cdot Q_{t} \to Q_{0} = 10 k g \cdot 0 \frac{m}{s} \to Q = t \cdot Q_{t}$ $Q = Q_0+t*Q_t -> Q_0 = 10kg * 0m/s -> Q = t*Q_t$
$Q_{t} = F \to Q = t \cdot F \to Q = 10 s \cdot 50 N \to Q = 500 N \cdot s$ $Q_t = F -> Q = t*F -> Q = 10s*50N -> Q = 500N*s$ //

Hope it helps.

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How does acceleration affect momentum?

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