A little bit of physics (for what it's worth):
Speed and velocity are two different things. Speed is independent of direction, but velocity is a specific speed in A SPECIFIC DIRECTION (e.g. a Vector Quantity).
Acceleration is, in simple terms, defined as a change of velocity. Since velocity has size and direction, it doesn't necessarily mean an increase in speed. Performing a turn at constant speed can be acceleration by virtue of the change in direction alone.
Thus acceleration can be (i) change in speed in a straight line, (ii) change in speed and direction or, (iii) change in direction at constant speed.

Of course in normal piloting terms we talk about speed in knots, be it IAS or TAS, etc. But if we are talking about the physics of an aircraft in flight we should consider it's velocity (i.e. speed AND direction) in order to make sense of the effects of acceleration.