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.