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

• Always >= 0 (mass and $v^2$ are non-negative)
• Scalar quantity
• Frame-dependent (different observers measure different KE)
• Dimension: [ML^{2T}^{-2}]

KE-Momentum Relation: p = mv, so KE = p^$\frac{2}{2m}$ or p = sqrt(2mKE)

Useful Deductions:

1. For same KE: $p_1$/$p_2$ = sqrt$\frac{m_1}{m_2}$ — heavier body has more momentum
2. For same momentum: $KE_1$/$KE_2$ = $\frac{m_2}{m_1}$ — lighter body has more KE
3. If p is doubled, KE becomes 4 times
4. If KE is doubled, p becomes sqrt(2) times

Percentage Change: If v increases by n%, KE increases by approximately 2n% (for small n). Exact: $KE_{new}$/$KE_{old}$ = (1 + n/100)^2