Engine and Vehicle Physics

A car engine of power P at speed v exerts force: $F_{\text{engine}} = \frac{P}{v}$

At terminal velocity (constant speed), F_engine = F_drag. The engine power is entirely spent overcoming drag: $P = F_{\text{drag}} \times v$

As speed increases at constant P, driving force decreases. Maximum speed is where the entire power overcomes air resistance.

Pump Efficiency

Rate of lifting water of density ρ, flow rate Q ($m^{3}$/s), to height h: $P_{\text{useful}} = \rho g Q h \quad (\text{W})$

$P_{\text{input}} = \frac{\rho g Q h}{\eta}$

Human Body Power

• Typical resting metabolic rate: ~80 W
• Walking briskly: ~200–300 W
• Sprint: ~1000 W (briefly)
• Tour de France cyclist: ~400 W sustained

These show that 1 hp ≈ 746 W ≈ power of a very fit athlete working flat-out.

Energy Units Context