Originally Posted by
pickslides Happy to kick it off for you
$\displaystyle \frac{dv}{dt}=-kv^{1/2}$
separating the variables you get
$\displaystyle \frac{dv}{v^{1/2}}=-k~dt$
Now integrate both sides
Hint: $\displaystyle \int \frac{dv}{v^{1/2}} = 2v^{1/2}$