Work–Energy Theorem

Work-energy theorem: net work done on a body equals its change in kinetic energy.

W_net = K_f − K_i = ½m(v_f² − v_i²).

Applies to any net force — constant, variable, gravity, friction, spring, etc.

Derived directly from Newton's 2nd law integrated: F = m·a ⇒ ∫F·dx = ∫ma·dx = ∫mv·dv = ½m·Δ(v²).

Useful for solving problems WITHOUT explicit time analysis — only initial and final states matter.

If multiple forces act, W_net = sum of works done by each (or work by the net force).

Power form: P = dW/dt = F·v.

Used in projectile, pendulum, spring-block, collision, friction-on-incline problems.