A block is projected up an incline with speed Vo, find the time it takes to return to its initial position. The angle of incline is θ and coefficient of friction μk. So I figured this problem has to be done in two parts. I integrated through F=ma to find the time it takes from vo to v=o when the block comes to rest. Then I integrated to find the distance it traveled x to reach that point. I figured all I would have to do now is integrate over the distance x but in the other direction with the coefficient of friction now in the opposite direction since the block is moving back down to it's initial position.. So here is my problem. I wrote dx2/dt2 = -gsinθ+μkgcosθ and I have x=Vo2 / 2(gsinθ+μkgcosθ) for the distance travelled. How do I find time? I can't just integrate twice to get x from dx2/dt2.. My calculus knowledge is failing me at the moment. Any help would be greatly appreciated.