Mechanical Power

The power is defined as work per time and therefore equal to the derivative $$\boxed{P = \frac{\mathrm{d}W}{\mathrm{d}t}}$$ The same formula can be used if the energy $E$ is given: $$P = \frac{\mathrm{d}E}{\mathrm{d}t}$$ Inserting the correlation $E=\vec{F}\cdot\vec{s}$ into $E$ and using $\mathrm{d}\vec{s}/\mathrm{d}t = v$, the following formula can be obtained: $$\boxed{P = \vec{F}\cdot\vec{v}}$$