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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! *[Watch Your Head]* ({excerpt-include:Watch Your Head|nopanel=true}){panel}