Dimensional Formula of Power — [ML²T⁻³]

Method 1: From P = W/t (Power = Work / Time)

Dimensions of Work: • W = Force × displacement = [MLT⁻²] × [L] = [ML²T⁻²]

Dimensions of Time: • t = [T]

Therefore: [P] = [W]/[t] = [ML²T⁻²]/[T] = [ML²T⁻³]

Method 2: From P = F × v (Force × velocity)

• Force (F) = [MLT⁻²] • Velocity (v) = [LT⁻¹]

[P] = [MLT⁻²] × [LT⁻¹] = [ML²T⁻³] ✓

Both methods give: [ML²T⁻³]

SI Unit: • Power unit = Watt (W) • 1 Watt = 1 Joule per second = 1 J/s • In dimensional terms: kg·m²·s⁻³

Definition: Power = Work done per unit time = Rate of doing work P = W/t = F·v = E/t

Units of power: • SI unit: Watt (W) — named after James Watt • 1 kW (kilowatt) = 1000 W • 1 MW (megawatt) = 10⁶ W • 1 horsepower (hp) = 746 W ≈ 750 W • 1 kWh (kilowatt-hour) = unit of energy (3.6 × 10⁶ J) — not power

Relation between energy and power: • Energy = Power × Time • [E] = [ML²T⁻²] = [ML²T⁻³] × [T] = [ML²T⁻²] ✓

Comparison of dimensional formulas: Quantity | Dimensional Formula Power | [ML²T⁻³] Work/Energy | [ML²T⁻²] Angular Momentum | [ML²T⁻¹] Pressure/Stress | [ML⁻¹T⁻²] Force | [MLT⁻²] Velocity | [LT⁻¹]