Work, Energy and Power — Formula Sheet

W = F S \cos\theta

W = \int_{x_i}^{x_f} F(x) \, dx

KE = \frac{1}{2}mv^2

PE_{grav} = mgh

PE_{spring} = \frac{1}{2}kx^2

W_{net} = \Delta KE

P = \frac{W}{t}

P = F \cdot v

Work done by a constant force is given by the dot product

W = F·S = FS cosθ.

For variable forces, work is calculated using integration

W = ∫F(x)dx.

Kinetic energy (KE) is the energy of motion

KE = ½mv².

Work-Energy Theorem

Net work done on an object equals its change in kinetic energy: W_net = ΔKE.

Elastic potential energy

PE = ½kx² (in springs).

Power is the rate at which work is done or energy is transferred: P = W/t.

Its SI unit is watt (W), where 1 W = 1 J/s.