What kind of movement is it? Is it steps (a pedometer)? If it is, just count the steps and multiply by the step length. Apologies for the obvious anwer here). If not, then things are rather difficult as you will get nowhere trying to apply Newton's Laws of motion x=v*t for a=0 and x=a*t^2/2 for constant a, as (i) the SNR is poor for low values for acceleration, and (ii) the value of the acceleration a might be changing all the time and (iii) you will need an XYZ accelerometer if the movement is not alligned with the axis where you measure the acceleration... Not as trivial a matter as Newton Laws of Motion might suggest, in practice.
Mehdi, if i understand your question correctly you are trying to determine distance while measuring acceleration. If this is correct then you need to double integrate the acceleration with respect to time to get distance.
To add to Stephen's answer, you can do this, but need to be aware of drift when performing double integration. If you are trying to calculate large distances then, due to the accumulation of small errors you will get results that are not entirely accurate. You can observe this if you take a reading from a still accelerometer and integrate the signal twice.