Work, Energy & Power

Energy is the capacity to do work; it is conserved — never created or destroyed, only transferred.

Work and energy

Work done $W = Fs\cos\theta$ (J), where $\theta$ is the angle between force and displacement.
Kinetic energy $E_k = \tfrac12 mv^2$.
Gravitational PE (change) $\Delta E_p = mg\Delta h$.

Worked example. A $1000$ kg car speeds up from $10$ to $20$ m s⁻¹. Gain in KE $= \tfrac12 m(v^2 - u^2) = \tfrac12 (1000)(400 - 100) = 150\,000$ J $= 150$ kJ.