Kinetic Energy

$KE = \frac{1}{2}mv^2 \quad [\text{M}^1\text{L}^2\text{T}^{-2}]\ (\text{J})$

• Always ≥ 0 (scalar)
• Depends on $v^{2}$ — doubling speed quadruples KE
• In terms of momentum: $KE = \frac{p^2}{2m}$

Momentum Form — Critical Comparisons

Work-Energy Theorem

$W_{\text{net}} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$

"Net work" = algebraic sum of work done by ALL forces: $W_{\text{net}} = W_{\text{gravity}} + W_{\text{friction}} + W_{\text{applied}} + W_{\text{normal}} + \cdots$

This theorem is ALWAYS valid — with or without energy conservation.

Common Errors to Avoid

1. Forgetting friction when the surface is rough
2. Including normal force as doing work (it usually does W = 0)
3. Assuming the theorem applies only to the net force (not summing individual works)