Power¶
Time rate at which work is done
The average power
\[
P_{\text{av}} = \frac{\Delta w}{\Delta t}
\]
\(\Delta w\) is the average quantity of work done
\(\Delta t\) is the time interval
Units of Power¶
\[
\text{Wat} = \frac{\text{Joule}}{\text{second}}
\]
Instantaneous power¶
\[
P = \lim_{\Delta t \rightarrow 0} \frac{\Delta w}{\Delta t}
\]
If forces act on a moving object, we can express the corresponding power in terms of force and velocity:
\[
P_{\text{av}} = \frac{F_{\parallel} \Delta s}{\Delta t} = F_{\parallel} v_{\text{av}}
\]
\(\Delta s\) is the magnitude of displacement \(\Delta \vec{s}\)
Int the limit we get the instantaneous work:
\[
P = F_{\parallel} v
\]