# Newton's second law of motion and impulse

** Force ** and ** impulse ** are closely related concepts. Impulse is normally defined as the change in momentum, but it can also be defined in terms of force.

An impulse of $$10 \text{ kg m/s}$$ could be the result of a force of $$1 \text{ N}$$ applied over $$10 \text{ s}$$ or of a force of $$10 \text{ N}$$ applied over $$1 \text{ s}$$.

If mass and force are constant during the period of impact, the impulse is also directly proportional to the force and the change in velocity: $$$\vecphy{J}=\Delta \vecphy{p}=\vecphy{F}t$$$ This can be shown as follows: $$$ \begin{align*} \vecphy{J}&=\Delta\vecphy{p}&\quad\quad \vecphy{F}&=\frac{d\vecphy{p}}{dt}&\\ &=\vecphy{p}_1-\vecphy{p}_0&\quad\quad &=\frac{\Delta\vecphy{p}}{t}&\\ &=m(\vecphy{v}_1-\vecphy{v}_0)\\ &=m\Delta\vecphy{v}\\ \Rightarrow\vecphy{J}&=\Delta\vecphy{p}\\ &=\vecphy{F}t \end{align*} $$$