Accelerometers measure acceleration: a change of speed - not the speed.
If you want to measure 3 mins. acceleration (seeing a value) - it works just on a rocket:
just a rocket would increase its speed over a period of 3 minutes.
Acceleration value 0 does not mean the object has stopped, is not in motion: it just means: the speed does not increase (or decrease) anymore. The velocity is constant.
You can just assume the object has stopped again when you saw the exact same amount of negative acceleration (braking) after a positive acceleration (speeding up). Then, object is back to same speed as before (but it does not mean stationary, when staring point was already a constant velocity).
BTW:
I would consider 3-axis calculation: use vectors in order to know how your object is moving in a 3D space. If you ignore other axis - your result is wrong: if it moves mainly in X, but also a bit in Y direction (or just in Z direction), the vector for X only taken is wrong: the speed of the object is for sure much larger (in 3D space) - consider a 3D vector.
In order to know the speed (and distance), you have to know the inertia (mass) of your object: if you measure the acceleration, combined with its mass - you can calculate the speed (change) and with it the distance it has traveled.
If you ignore any tiny acceleration - you get completely off: even a small speed change - ignored, can result in massive errors: acceleration of 1 over a period 3 minutes might end up in object is now moving with miles per hours after 3 minutes.
So, 20 from accelerometer can be drastic speed change. Any value not 0 tells you: the object is speeding up, getting faster and faster.
Acceleration measurement is "inertial navigation": any not zero value means: it gets faster, the speed changes, it moves even faster over a distance. It is "DELTA calculation": is the same amount of acceleration (integrated over time) the same as de-acceleration: then the object might have stopped (when it was stationary), or is back to original velocity. If the values for "speed up" and "break" are not the same: the system has entered a new different speed, but it keeps going to move.
The tiniest bit of acceleration tells you "there was a speed change". It is 3D space math. And with inertia (mass) considered - you can predict speed, distance and where it should be now (when starting condition is known).
Just acceleration value does not tell you anything, except: "it changes its speed".
And zero acceleration does not tell you it has stopped: just if up and down are equal values. Otherwise it keeps moving with the new (constant) speed.