Well, why not begin by trying to find a piece of land that is opposite other land? It is not as easy as you might think!

Nor is it easy to find means to create or support a tunnel at all.

Anyway, you would reach terminal velocity within at most a couple of hundred metres (not kM!) so thatyour momentum past the centre would be negligible unless you impossibly evacuated your impossible tunnel first. You would cook long, long (thousands of km long) before you reached the centre. If your tunnel worked, your only stable position would be at the centre. Because of Coriolis forces, the only way to avoid being abraded to mush on the way down would be to drill the hole from pole to pole.

In short, don't do it.

If it were somehow possible to make a tunnel capable of surviving extreme heat and pressure and you were not too bothered about coming out alive, you would fall towards the centre and, depending on the amount of friction, either slow down and stop somewhere near the centre as the resultant gravitational force decreases, or have enough momentum to continue past the centre, but stop before reaching the other side and keep oscillating until you slow down enough to stop at the centre.

You would die if you jumped in it because the gravity will push you side to side forever,if you want to have a clearer image of this,draw a stick man on a circle and lots of buildings on it,draw another stick man on the other side but not standing on the circle,exactly the oppisite: if the stick man were alive,it would find himself upside down on the other side,then die of blood rushing to his head.

You might find it entertaining to think what would happen if instead of having an iron core, the Earth were hollow. (Nicely, symmetrically hollow!) Would you fall towards the wall of the cavity, or the centre, or what?

And if you were to dig down towards the centre, would your weight change on the way down? (After all we can neglect the effect of your digging; the Earth's mass doesn't change in the process.) If it were to change on the way down, where would it be at its maximum? At the surface? Halfway down? At the centre? All the way down?

Let's assume it is an insulated and evacuated tube passing through the centre of the Earth. Release a mass at the surface and it will behave like a pendulum, accelerating up to the centre then slowing till it comes to rest on the other side at the surface, before falling back again, for ever.