I have a similar interest in using consumer technologies for research purposes! Here are some sources I found regarding smart phone accelerometers (attached). Hopefully, they include the level of detail you're looking for!
Can you clarify your question a bit more please? Are you interested in the actual trace provided by the accelerometers when using them for activity monitoring purposes? Can you also clarify what you mean by "acceleration is fixed" please?
Generally speaking, the accelerometer in the phone will show the acceleration forces that the phone is subjected to. If it is attached to a person, it will show the acceleration of the body part to which it is attached. For walking and jogging type activity you would expect to see a great deal of movement in the accelerometer signal corresponding with the movement of the person.
I assume the accelerator that you mentioned is the type of external sensing device to be worn on the user body parts, that can automate tracking and recording the movement data, and transferred to the smartphone by signals through some form of connection.
if the context is coherent in manner with yours, thus the readings of the accelerator on smartphone can be vary in several aspects
Variation in usability of the device among users. this includes the level of compliance in wearing the device, appropriateness in wearing the device, incorrectly operating the device.
Variation in quality of the device within itself. this include the accuracy in movement detection (account sensitivity level), precision in types of movement detection (the degree to which it can discriminate different types of movement engaged), occurrence of miscalibration.
Variation in smartphone device used among the participants. Different smartphone manufacturer incorporate different operating system platform to support the accelerometer, hence variation in compatibility of the device especially the data transfer via signaling through communication network. Availability of the network sensing without interference within acceptable geographical radius, allow data to be transferred smoothly and in real-time manner. Since the measurement has temporal domain, variation in timing of reception of the data captured from the accelerometer to smartphone may account some variation in the degree of latency.
Variation in terms of the presence of conditioning effect brought by monitoring device to the users such as Hawthorne effects, which is subjected to the awareness level of being monitored / tracked.