Imagine that a certain engine can cause the road to exert a certain maximum forward force $\left|\vec{F}_{S F}\right|$ on a certain car. If we change the car's design to reduce its drag coefficient by a factor of 2 , by what factor will the car's maximum speed increase (other things being equal)?
A) No increase
B) 1.41
C) 2
D) 4
E) Depends (specify)
F) Other (specify)

Question

Quizplus · Accepted Answer

The maximum speed of a car is limited by the drag force, which is proportional to the square of the speed. Reducing the drag coefficient by a factor of 2 means the force due to air resistance at a given speed is halved. To achieve the same drag force (and thus the same limiting factor for maximum speed) at a higher speed, the speed must increase by the square root of 2, or approximately 1.41.

Imagine That a Certain Engine Can Cause the Road to Exert