Hypothetical

[Bridge]

If you're falling to the core, you'll deccellerate nearing the center since gravity at the other side also pushing you at the same time. This force pushing you down will be overwhelmed by the force propelling you up as you got near the center.

Is this really how it works? I thought gravity only worked in 'one' direction, but... I was gonna use a magnet as an example but then I realised that a magnet follows the rules you just said.

I think gravity does work like that, as you said, in one direction. Hypothetically, if you could pass through the core unscathed, I think it is generally accepted that you would swing back and forth, gradually losing momentum until come to a full stop at the center. If you had absolutely no mass then I suppose it would happen as JAP said, but I don't think earth's gravitational forces are strong enough to bring your momentum down to zero instantly at the center. Could be completely wrong though.