[Hoodat]

You accelerate all the way to the center then begin to slow as you pass it.

Correct. Maximum velocity would be achieved as the object passes through the center. The maximum rate of acceleration (from x to y) would be realized at the start. The initial acceleration would be 9.8 m/s². At the earth's center, it would be zero, and at the opposite end of the earth, it would be -9.8 m/s².

The object would not begin to slow until acceleration goes negative which would occur just after passing through the center point.

[cripplecreek]

Also, down would be come up as you passed the center.