Hi everyone. I just began my Calculus based physics course 3 weeks ago and I really love it. I've been going ahead of the class though and came across the following problem: As g, the acceleration due to gravity, is constant for only a limited range of height distances, a better approximation would be the linear equation a(h) = g - hg' where h is the distance from the ground and g' is a small constant of proportional dimensions. My problem is that I now need to derive velocity as a function of distance, and then as a function of time. I've tried everything I can think of, but I just can't seem to wrap my head around how I can express height as a function of time, or vice versa, without knowing either acceleration as a function of time or velocity as a function of time, but I can't get either of those without knowing one of the other two!!!! Any help would be greatly appreciated. Thanks in advance.