Thinking about the space shuttle

It all depends on the rate at which fuel is being burned.
But if, as you say, that is constant, then the accelerating force is constant but the mass of the rocket/fuel combination is decreasing, hence the acceleration is increasing.
Since the mass being accelerated is no longer constant then newton's 2nd law is written as,

F = d(mv)/dt

 

The acceleration of any rocket (or any vehicle) depends on the thrust (force) and mass.

As propellant mass decreases with consumption, the acceleration for a given thrust increases.

In addition, as the force of gravity and atmospheric drag decrease with altitude, the acceleration increases.

Finally, the Shuttle has variable thrust motors. The main engines (SSMEs) throttle down when the Shuttle approaches maximum hydrodynamic load on the structure. I was during this phase when Shuttle Challenger exploded.

So the acceleration generally increases, with short periods of decrease.

At orbit, the Shuttle ceases to accelerate radially but since it is orbit, its velocity is constantly changing direction, so it is constantly accelerating in that regard.

 

On an interesting tangent

Speaking of thrust:

Going off the point slightly (but on an interesting tangent), I know that with Ion Engines the optimum power usage is obtained if you vary the thrust as the fuel is used up so that the acceleration is constant (hence decreasing the thrust with time).

There is also with ion engines and so I would assume with regular rockets optimum exhaust velocities for the propellant. So different exhaust velocities for a given mass of fuel will result in different terminal velocities.

[I just thought I would include this... as I haven't yet contributed so many posts to PF]