# Impulse as the product of force and time.

Suppose a force \overrightarrow F acts for a small-time dt. The impulse of the force is given by

\operatorname d\overrightarrow J=\overrightarrow F\;\operatorname dt

If we consider a finite interval of time from t_1 to t_2, then the impulse will be

\overrightarrow J=\int\operatorname d\overrightarrow J=\int_{t_1}^{t_2}\overrightarrow F\;\operatorname dt

If {\overrightarrow F}_{av} is tne average force, then

\overrightarrow J=\int_{t_1}^{t_2}\overrightarrow{F_{av}}\;\operatorname dt=\overrightarrow{F_{av}}\int_{t_1}^{t_2}\operatorname dt

or, \overrightarrow J=\overrightarrow{F_{av}}\times\triangle t, where \triangle t=t_2-t_1

Thus, the impulse of a force is equal to the product of the average force and the time interval for which it acts.

Dimension of impulse = \left[MLT^{-1}\right]

SI unit of impulse = kg\;ms^{-1}

CGS unit of impulse = g\;cm\;s^{-1}