I made a rudimentary program that "integrates" acceleration for velocity (assuming that v at t = 0 is 0):
velocity_from_accelerometer (2).aia (3.0 KB)
It takes the sum of the acceleration for 100ms, and multiplies it into the time period (again, 100ms), which gives the average velocity in that period of time.
I also subtract g (acceleration due to gravity) from aₓ (vertical acceleration component).