?

Classical Mechanics

Free Version

Upgrade subject to access all content

Difficult

Drifting Kayak

CLMECH-RJN4C1

A woman in a kayak stops paddling when the kayak has a speed of $v_0$. As the kayak drifts through the water, it experiences a resistive force from the water of $F = -bv$, where $b$ is a constant and $v$ is the instantaneous speed of the kayak. Assume the kayak is only moving horizontally and in a single direction. Which of the following expressions correctly states the speed of the kayak as a function of time?

A

$v = e^{-\frac{b}{m}t}$

B

$v =\frac{v_0}{1 + \frac{b}{m}t}$

C

$v = v_0e^{-\frac{b}{m}t}$

D

$v = v_0(e^{-\frac{b}{m}t} - 1)$