A Ball accelarating down a hill

You can only do straight integration/differentiation to convert between displacement, velocity and acceleration when integrating/differentiating with respect to t(ime).

*Edit* Are you trying to find the velocity? Do what was said above.

And that's the velocity at any given value of x... or something else?
I think I worded my first question poorly/didn't have a solid idea of what I was asking, so I'll try re-wording it.

A hill is modeled by a continuous function f(x), where y is the height above level ground. If you let an object freely fall down, starting at the point (x,y) on the function, how fast will it accelerate, how fast will it move(velocity), and how much distance/displacement will it travel*, relative to t. Ignoring friction, drag, and a rotation vs sliding.

*Would this just be the length of the line making the function, or something else. Like if the function gets too steep for the object to be held onto it via gravity... Though that would depend on previous velocities... this is getting complicated...