Asked by John Ng

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.

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. - ∞

Answers

Answered by oobleck
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.
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