Question

Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is double, then the maximum speed of the car.

• A. is unchaged
• B. increases by a factor of $\sqrt{2}$
• C. is also double
• D. increases by a factor of four.

Answer 1

The correct option is B increases by a factor of $\sqrt{2}$

It is given that

$F\propto v$

$F=kv.........\left(1\right)$

$v=\frac{F}{k}...........\left(2\right)$

$\because F=\frac{P}{v}.........\left(3\right)\left(given\right)$

$put\left(3\right)in\left(2\right)$

$v=\frac{P}{vk}$

$v^2=\frac{P}{k}$

$v=\sqrt{\frac{P}{k}}.........\left(4\right)$

If output power

$P^{\prime }=2P$

Then,

$v^{\prime }=\sqrt{\frac{P^{\prime }}{k}}$

$v^{\prime }=\sqrt{\frac{2P}{k}}$

$v^{\prime }=\sqrt{2}v(\because v=\sqrt{\frac{P}{k}})$