Answer
The maximum velocity occurs when $v=10 \ ft/sec \ $, which occurs at $\dfrac{dv}{dt}=0$.
Work Step by Step
We start with the force equations
$F=F_p-F_r$
$m \dfrac{dv}{dt} =50-5v $
This implies that $\dfrac{dv}{dt}=\dfrac{50-5v}{m}$
When $\dfrac{dv}{dt}=0 $, so
$50-5v =0$
This implies that $v =10$
Therefore, the maximum velocity occurs when $v=10 \ ft/sec \ $, which occurs at $\dfrac{dv}{dt}=0$ .
