1. The problem statement, all variables and given/known data Suppose we had a straight tunnel, through Earth's center, to a point on the opposite side of the planet, and used it to deliver mail to the other side. With what speed would our packages pass through Earth's center. 2. Relevant equations ag = (GM)/R2 Mins = (4/3)πR3*ρ 3. The attempt at a solution So, I'm assuming (but not completely sure) that the question is asking for the man's speed at the center (but again, I could be interpreting the question completely wrong. Either way, I'm still stuck on how to solve it.) I figured that I could take the integral of ag with respect to R (since the distance from the center of the earth is continuously changing as you pass through the center.) So: ag = ∫[G*ρ*(4/3)π *R3]/R2 (from 0 to R) My problem here is that ρ is just M/V which is 3M/(4πR3), which basically cancels out a whole bunch of R's and leaves you with: ag = GM∫[1/R2 (from 0 to R...I'll worry about signs later) AND: ag = GM/R, which doesn't actually work out since you end up having m2/s2, which is not acceleration. I know I probably messed up the integral, but I'm not sure how else you would solve this problem.