Impulse and Time-Averaged Force null
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:
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\begin
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[ \langle\vec
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\rangle_
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\equiv \frac{\int_{t_{i}}^{t_{f}}\vec
\:dt}{t_
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-t_{i}} ]\end
Using the definition of impulse, this expression can be written:
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\begin
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[ \langle\vec
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\rangle_
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= \frac{\vec{J}}{t_
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-t_{i}}]\end
null Watch Your Head (Consider the impulse and average force delivered to the head of a player performing a "header" in soccer. )