Please clarify the question. One way of doing this is to express the problem in mathematical notation.

we have calculated the acceleration due to gravity from a particular altitude down to the surface

If we assume an airless body (eg the Moon), and calculate the gravitational acceleration as a function of the radius from the center of the Moon:

Gravitational Acceleration = g(r).

g: gravitational acceleration

r: radius from center of the Moon

For "normal" velocities and "normal" masses, g(r) can be approximated by Newton's law of gravitation:

g(r) = GM/r2

Where:

G: Gravitational Constant

M: Mass of the Moon

r: radius from center of the Moon

Assuming that there is no tangential velocity (which could put it in an orbit that

*never *hits the Moon's surface), you calculate the final impact velocity v

_{f} by integrating this acceleration g(r) from initial radius R

_{i} to the Moon's radius R

_{m}, and adding any initial radial velocity v

_{i}.

what would happen if we accelerated an object down to the surface at exactly this rate of increasing acceleration?

Here I am confused. If we let the object free-fall, it would experience acceleration g(r) without us having to do anything.

However, the active voice "we accelerated" implies that we do

*not* let if free-fall, but do something to it. What is this "something"?

Is it to double the acceleration? So the object accelerates at 2g(r)?

Are there unstated assumptions different from what I have assumed above?

Something else?