h3. Impulse and Time-Averaged Force [!copyright and waiver^SectionEdit.png!|Momentum (Average Force)]
[Impulse|impulse] and [force] are closely related. In fact, if a time interval of interest is specified, the [impulse] imparted by a specific [force] during that interval can be used to quickly estimate the time-average of that [force]. The mathematical definition of the time-average of a force is:
{latex}\begin{large}\[ \langle\vec{F}\rangle_{t} \equiv \frac{\int_{t_{i}}^{t_{f}}\vec{F}\:dt}{t_{f}-t_{i}} \]\end{large}{latex}
Using the definition of [impulse], this expression can be written:
{latex}\begin{large}\[ \langle\vec{F}\rangle_{t} = \frac{\vec{J}}{t_{f}-t_{i}}\]\end{large}{latex}
{panel:bgColor=#F0F0FF}!images^SAP.gif! *[Head-on Collision]* ({excerpt-include:Head-on Collision|nopanel=true}){panel}
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