3.5 Power

Power is the rate at which work is done or energy is transferred. It tells us how quickly energy changes form within a system.

Power is a scalar, measured in Watts (W), where ${1,W = 1,J/s}$.

Important Equation (Average Power): ${P_{avg} = \frac{W}{t} = \frac{\Delta E}{t}}$

${P_{avg}}$ = average power

${W}$ = work done

${\Delta E}$ = energy change

${t}$ = time interval

Example: If ${50,J}$ of work is done in ${2,s}$, the power output is: ${P_{avg} = \frac{50}{2} = 25,W}$

Instantaneous Power
For variable forces, the instantaneous power is the derivative of work with respect to time:

${P_{inst} = \frac{dW}{dt}}$

Substitute the definition of work: ${P_{inst} = \frac{d}{dt} \int_a^b \vec{F}(r) \cdot d\vec{r}}$

If the force is constant, this simplifies to: ${P_{inst} = \vec{F} \cdot \vec{v}}$

This final form is the most commonly used, expressing instantaneous power as the product of force and velocity when both are known.