# How does impulse affect momentum?

Jul 29, 2015

Impulse is mathematically equal to the change in momentum which happens during the action of the impulsive force (the force causing impulse).

#### Explanation:

From Newton's second law,

$\vec{F} = \frac{\mathrm{dv} e c p}{\mathrm{dt}}$

$\implies \vec{F} \mathrm{dt} = \mathrm{dv} e c p$
Integrating both sides,

$\vec{F} {\int}_{t {\text{_0)^t dt = int_(p}}_{0}}^{p} \mathrm{dv} e c p$

implies vecF(t - t""_0) = vecp - vecp""_0

By definition, impulse, vecJ = vecF(t - t""_0)

Thus, Impulse = Change in momentum