# 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?

**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:**

$\frac{{P}_{1}}{{P}_{2}}={\left(\frac{{v}_{1}}{{v}_{2}}\right)}^{3}\phantom{\rule{0ex}{0ex}}={\left(\frac{40}{80}\right)}^{3}\phantom{\rule{0ex}{0ex}}=\frac{1}{8}$

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