Acceleration is the measure of rate of change of velocity.
Speed and velocity measure time taken to move, but only velocity gives an extra factor. Direction.
If that direction changed at all, the acceleration would go up since the velocity had changed.
A time where acceleration would always change would be when a car goes around a roundabout. No matter if you stay at a constant speed, your velocity would change (changing direction), which would cause your acceleration to change too.
