The pattern we use with air resistance works on objects that are traveling on level ground, too. For example, if you stop pedaling your bicycle and just coast on a straight, level road, eventually you'll coast to a stop. The resistance here is proportional to your velocity, just like it is for a falling body.

Question

The general differential equation for coasting to a stop is (dv/dt ) = -kv
where k is a constant. What's the terminal velocity in this case?

a. 0
b. v

c. k

d. –k

e. - ∞

Answer 1

dv/dt = -kv
dv/v = -k dt
ln v = -kt
v = e^(-kt)

Terminal velocity happens as t→∞, so it is zero (assuming k>0, which should have been stated)

But then, we already knew that, right? The bicycle doesn't keep on rolling forever.