Prove, using unit analysis, that the formula for kinetic energy, E = ½mv², is dimensionally valid given that the unit of energy is the joule (J) = kg·m²·s⁻².

Question

Accepted Answer

RHS unit: ½ is just a number (no unit), so we consider mv². Unit of mass (m) = kg. Unit of velocity (v) = m·s⁻¹, so unit of v² = m²·s⁻². Therefore, unit of mv² = kg × m²·s⁻² = kg·m²·s⁻². LHS unit: Energy (E) = joule (J) = kg·m²·s⁻² (given). Since LHS unit (kg·m²·s⁻²) = RHS unit (kg·m²·s⁻²), the formula E = ½mv² is dimensionally valid.