Question

The drag force pushes opposite your motion as you ride a bicycle. If you double your speed, what happens to the magnitude of the drag force?

Answer 1

The drag force is directly proportional to the square of the velocity of motion of the object. So as the speed is doubled, the magnitude of drag force will get quadrupled.

Explanation:

Drag force is the opposing or resisting force acting on any object by the medium in which it is moving. So in this case, you are riding a bicycle, thus the medium can be considered as air.

The formula for calculating drag force is as below:

               $\text {Drag force }=\frac{1}{2} \rho v^{2} C_{D} A$

Here, ρ is the density of the air molecules, v is the velocity or speed of the bicycle, CD is the drag coefficient and A is the area of the bicycle.

In the above equation, only the term velocity will be a varying quantity with respect to time and other quantities will remain constant throughout the single situation of riding of bicycle.

So, the equation can be,

             $\text { Drag force }=k v^{2}$

Where ,  

     $k=\frac{1}{2} \rho C_{D} A$ (constant for this whole condition)

Now given the speed of bicycle increased from v to 2v, so the initial drag force will be

                   $N_{i}=k v^{2}$

After increase in speed, the final drag force will be  

                   $N_{f}=k(2 v)^{2}$

                   $N_{f}=4 k v^{2}=4 N_{i}$

Thus, if the speed of the bicycle is doubled, the drag force will get increased by four times.