Question

A moving car encounters air resistance which is proportional to the square of the speed of the car.What is the ratio of the power required at 40 km/hr to that required at 80 km/hrwith the same braking force?

Answer 1

The expression for power in terms of force and velocity:

$P=Fv$

But, it is given that $F\alpha v^2$

Hence, $P\alpha v^3$

Ratio of power:

$$\begin{gathered} \frac{P_1}{P_2}={\left(\frac{v_1}{v_2}\right)}^3 \\ ={\left(\frac{40}{80}\right)}^3 \\ =\frac{1}{8} \end{gathered}$$