Take the accelerometer and tip it over on it's side (or back, or front, or the other side) and take another reading. It should either read A minimum or maybe go to A maximum.

Just because something is MOVING doesn't mean it's ACCELERATING.
An elevator only ACCELERATES to get MOVING (or DECELERATES to come to a stop and/or reverse the direction it's MOVING).
Once it's MOVING, it's probably no longer ACCELERATING.

I'd doubt an elevator takes 10 seconds to ACCELERATE to it's maximum speed. 5 seconds, maybe, 10 seems like quite a long time to ACCELERATE.