Solution to 1996 Problem 31

If we let the downward direction be the positive x direction, then the equation of motion is
\begin{align*}m \ddot x = m g - b \dot x\end{align*}
With the initial condition that \dot x (t = 0), this differential equation can easily be solved for \dot x:
\begin{align*}\dot x =  mg/b \left(1 - e^{-t b/m}\right)\end{align*}
Thus, we can see that the answer (E) is correct.

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