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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: $$$ \begin{align*} \vecphy{J}&=\Delta\vecphy{p}&\quad\quad \vecphy{F}&=\frac{d\vecphy{p}}{dt}&\\ &=\vecphy{p}_1-\vecphy{p}_0&\quad\quad &=\frac{\Delta\vecphy{p}}{t}&\\ &=m(\vecphy{v}_1-\vecphy{v}_0)\\ &=m\Delta\vecphy{v}\\ \Rightarrow\vecphy{J}&=\Delta\vecphy{p}\\ &=\vecphy{F}t \end{align*} $$$

The magnitude of impulse is given by the area under the graph of force $$(\vecphy{F})$$ against time $$(t)$$
The magnitude of impulse is given by the area under the graph of force $$(\vecphy{F})$$ against time $$(t)$$