I never did like these "word" problems. The way I understand the problem, "acceleration" being the change in velocity per time, things will go faster or slower when in constant acceleration. Under constant accelerations, velocities will increase or decrease. So, A and B are out.
Constant velocity would mean there is no change in velocity. Thus, acceleration is still constant, just acceleration = 0. The acceleration doesn't change; it stays at 0. So, C is out.
For D, a change of direction doesn't necessarily mean there is a change of acceleration. It doesn't necessarily mean there isn't a change of acceleration. However, there would definitely be a "change in acceleration in a specific direction". For instance, if you are travelling east at an acceleration of 10 ft/sec2, then immediately start going north at the same acceleration, your acceleration "east" went from 10 to 0 with the change of direction. And, your acceleration "north" went from 0 to 10 with the change of direction. So, the answer is D, again, how I read the problem.
The speed of an object is the distance traveled by the object in unit time. Speed is scalar and direction is not of relevance here. Velocity of the other hand is a vector and is the rate of change of the object's position. Velocity is the displacement in unit time.
Acceleration is the rate of change in an object's velocity. The change could be either in magnitude of velocity or direction of velocity.
A change in direction is possible only when the object is accelerating, similarly the speed of increases or decreases only when the object is accelerating.
There is no acceleration when the object is moving at a constant velocity.