Cool. I'd always assumed you'd slow down and rest at the center.
You accelerate all the way to the center then begin to slow as you pass it. You slow to the apex right at the surface on the other side.
Aside from the impossibility of it, it would be a great transportation method. Maybe it would work on geologically inactive moons.
I once saw a heavy tool let loose into the bore of a powerful MRI magnet. Bearing in mind that the center of the magnetic field is in the very center of the bore, the tool shot through to the other end then came back, oscillating several times before coming to rest in the center. It was as frightening as it was cool to watch. BTW, the idiot who brought a magnetic tool into the room was kicked off the job.