Answer to Question #132417 in Mechanics | Relativity for Alfraid

Question

Derive the relation between impulse and momentum.

Answer 1

Using the Newton's second law:

$\vec{F}=m\frac{d\vec{v}}{dt}$

We can rewrite it as:

$\vec{F}dt=md\vec{v}$ $\int\vec{F}dt=\int md\vec{v}$ $\vec{F}\Delta t=m\Delta \vec{v}$

Which is by definition of impulse and momentum:

$\vec{J}=\Delta \vec{p}$

So, the impulse equals to the change of momenta.