# Math Help - [SOLVED] Aerodynamic drag force and max speed?

1. ## [SOLVED] Aerodynamic drag force and max speed?

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

A)is unchanged
B)increase by a factor of sqrt.(2)
C)is also doubled
D)increase by a factor of four

2. Originally Posted by fardeen_gen
Assume the aerodynamic drag force on a car is proportional to the speed.
But its not, at high speed we are in the high Reynolds number regime so drag is approximatly proportional to the square of speed.

If the power output from the engine is doubled, then the maximum speed of the car:

A)is unchanged
B)increase by a factor of sqrt.(2)
C)is also doubled
D)increase by a factor of four
At maximum speed assume aerodynamic drag $D(v)$ is the dominant retarding force, then we have the work done by the engine when the car moves through a distance $\Delta x$ is:

$\Delta W=D(v) \Delta x$

so the power required is the rate at which work is done so if the time to move through $\Delta x$ is $\Delta t$:

$P(v)=\frac{\Delta W}{\Delta t}=D(v)\frac{\Delta x}{\Delta t}=D(v)v$

Now we are told to (erroneously) assume that $D(v)=kv$, so:

$P(v)=kv^2$

So doubling the power will support a maximum speed $\sqrt{2}$ times what it was before.

CB

3. Thank you!