OK I have a slightly new problem that seems much more difficult.

$\displaystyle X'(t) = \mu_{k}gt + \frac{A}{4m} \int X'(t)^2dt$

constants:

$\displaystyle \mu_{k}$ = kinetic friction coefficient

$\displaystyle g$ = gravity

$\displaystyle A$ = cross sectional area

$\displaystyle m$ = mass

I am trying to solve $\displaystyle X(t)$ and then solve the specific function as an initial value problem.

I just need help solving $\displaystyle X'(t)$ for now. I should be OK after that.

Thanks

This is for a hobby physics project, not for homework.