v (dv/dx) = - (1/250) vē - g
solve the equation for v as a function of x
this is for upward motion using quadratic model of air resistance
thanks
Is $\displaystyle g$ a constant?
If so...
$\displaystyle v\,\frac{dv}{dx} = -\frac{1}{250}v^2 - g$
$\displaystyle \frac{dv}{dx} = -\frac{1}{250}v - gv^{-1}$
$\displaystyle \frac{dv}{dx} = -\frac{v}{250} - \frac{g}{v}$
$\displaystyle \frac{dv}{dx} = \frac{-v^2 - 250g}{250v}$
$\displaystyle \frac{dv}{dx} = -\frac{v^2 + 250g}{250v}$
$\displaystyle \frac{dx}{dv} = -\frac{250v}{v^2 + 250g}$
$\displaystyle \frac{dx}{dv} = -250v(v^2 + 250g)^{-1}$.
You can now solve this with a $\displaystyle u$ substitution.