The maximum useful output power of a car travelling on a horizontal road is P. The total resistive force acting on the car is kv2, where v is the speed of the car and k is a constant.

Question 42

The maximum useful output power of a car travelling on a horizontal road is P. The total resistive force acting on the car is kv², where v is the speed of the car and k is a constant.

 

Which equation is correct when the car is travelling at maximum speed?

A v³ = P / k                 B v² = P / k                 C v = (P/k)²                 D v = (P/k)³

 

Reference: Past Exam Paper – November 2019 Paper 13 Q17

 

Solution:

Answer: A.

Power = P

Resistive force F = kv²

For a body moving with constant speed,

Power P = Force × velocity

P = F × v

P = (kv²) × v

P = kv³

Make v the subject of formula,

v³ = P / k