Key Equations

Work done by a force over an infinitesimal displacement	$d W = \vec{F} \cdot d \vec{r} = \| \vec{F} \| \| d \vec{r} \| cos θ$
Work done by a force acting along a path from A to B	$W_{A B} = \int_{path A B} \vec{F} \cdot d \vec{r}$
Work done by a constant force of kinetic friction	$W_{fr} = − f_{k} \| l_{A B} \|$
Work done going from A to B by Earth’s gravity, near its surface	$W_{grav, A B} = − m g (y_{B} - y_{A})$
Work done going from A to B by one-dimensional spring force	$W_{spring, A B} = − (\frac{1}{2} k) (x_{B}^{2} - x_{A}^{2})$
Kinetic energy of a non-relativistic particle	$K = \frac{1}{2} m v^{2} = \frac{p^{2}}{2 m}$
Work-energy theorem	$W_{net} = K_{B} - K_{A}$
Power as rate of doing work	$P = \frac{d W}{d t}$
Power as the dot product of force and velocity	$P = \vec{F} \cdot \vec{v}$