Question

A Lamborghini Diablo hand an engine that could generate 530 horsepower. The cross-sectional area of the car is 2.2 m^2. The drag coefficient for the car is 0.26. Assume the density of the air is 1.29 kg/m^3. If the force of drag is the only force resisting the option of the car (ie. there are no other source of friction), what is the top speed of this car?

Answer 1

Drag Force is given by

D = (1/2)(C)(ρ)(v²)(A)

where C = drag co-efficient

ρ = Density of air

v = speed of the car

A = Cross-sectional area of the car

D = 0.5 * 0.26 * 1.29 * 2.2v²

D = 0.37v²

Power Loss due to Drag Force = D*v

P_loss = 0.37v³

For top speed :-

Power Loss = Max Power Generated

So
0.37v³ = 530 Horsepower

0.37v³ = 530 * 735.5 {1 Horse power = 735.5 watt}

0.37v³ = 389814

v^{3 =} 389814/0.37

v³ = 1053551

v = 101.75 m/s

v = 366.3 kmph