Question

You are driving and you double the velocity of your car. By what factor has the dragforce due to air increase?

Answer 1

The drag force in terms of the velocity is,

`F\propto v^2`

where v is the velocity of the car,

If the velocity of the car is doubled,

`v^(\prime)=2v`

Then, the drag force acting on the car is,

`\begin{gathered} F^(\prime)\propto v^(\prime2) \\ F^(\prime)\propto(2v)^2 \\ F^(\prime)\propto4v^2 \\ F^(\prime)\propto4F \end{gathered}`

Thus, the drag force becomes four times of its initial value.