> [!summary] Power is the rate of energy transferred over time. > **Key equations:** > Power expressed in energy: $P=\frac{dE}{dt}$ > Power expressed as force: $P = F(t)\cdot v(t)$ > Average power: $P = \frac{W}{\Delta t}$ >[!info]+ Read Time **⏱ 1 min** # Definition Power is the [[Rate of Change|rate]] at which [[Work|energy]] is transferred over time. It's the [[Instantaneous|instantaneous]] rate at which [[Work|work]] is being performed on an object. It is a [[Scalar & Vectors|scalar]] measurement in [[Watt|watts]]. Mathematically, power can be defined in many ways but most commonly as $ P = \frac{dE}{dt}= \frac{\vec{F(t)} \cdot \vec{dr}}{dt} = \vec{F(t)} \cdot \vec{v(t)} $ If the force was not constant, to determine the average power over time, integrating over time is needed like below. $\begin{array}{c} P_{avg} = \frac{P(t)}{\Delta t} \\ P_{avg} = \frac{1}{\Delta t} \int_t ^ T P(t)dt \\ P_{avg} = \frac{1}{\Delta t} \int_t ^ T \frac{F(t) \cdot dr}{dt} dt \\ P_{avg} = \frac{1}{\Delta t} \int_t ^ T F\cdot dr \\ P_{avg} = \frac{W}{\Delta t} \end{array}$ ![[wor_3.png]] [^1] >[!note] Explanation A force on a random object. [^1]: Taken from R. Epp Lecture notes.