Freefall

If you jumped into a hole in the center of the earth, how long would it take to come to a stop? --Sodium

I feel compelled to explain why this is not entirely practical. For one thing, it's entirely likely that such a hole would collapse, but let's assume it's lined with a magic extra-strong material that also keeps the tunnel from reaching temperatures of thousands of degrees. The air pressure would also be a problem. We currently have only 62 miles (100 kilometers) of air above our heads, so having several thousand miles of air about our heads would likely crush us.

With that out of the way, let's turn to the actual scenario. I'll assume that this tunnel is a vacuum (so that the air pressure doesn't crush the jumper [and because physicists like working in a vacuum]) and that it's sealed at both ends (so the tunnel isn't filled with wind). I'll also assume that your aim is good enough that you don't hit any walls, which would (obviously) kill you.

The exact formula for figuring this out is more complicated than traditional gravitational acceleration since the mass that's actually pulling on you will decrease as you approach the center of the earth.[1] On average, the jumper's acceleration will be about 5 meters per second squared, but it does change some.[2] I'll assume that the change in acceleration (jerk) is constant, even though it isn't, to simplify the equations. Because I'm lazy!

I can't resist going off-topic to describe some rather interesting facts. As everyone (who's read this far at least) knows that velocity, acceleration, and jerk are the 1st, 2nd, and 3rd derivatives of motion. What you may not know is that jounce (or snap), crackle, pop, lock, drop, shot, and put are the 4th, 5th, 6th, 7th, 8th, 9th, and 10th derivatives of motion, respectively. Just an awesome fact that was worth sharing. I don't know why anyone would use these though.

Anyway, back to business. I wrote a bit of code which tells me the average jerk and also tells me that it would take about 22 minutes to fall to the center of the earth. This implies that it would take 21 minutes, so my math can't be that far off. It doesn't really matter though, since your momentum would carry you all the way back up to the surface, at which point you'd just repeat it all over again.[3]

I wonder how long it would take for a person to get bored of falling assuming they didn't know that they'd never hit the ground...