Here's hopin' a response comes back soon.
It would be difficult for an accelerometer to detect linear motion if the object changes speed at a slow rate. Remember it only detects change in motion. (Imagine replacing the speedometer and trip counter in your car with a bar for your current brake and gas pedal position) The sensor will usually show -9.8 m/s^2 in the vertical axis (depending on it's orientation), this reading will not change while the device is in motion, but if it stops or starts in any given direction, you will see a momentary change in the reading. This method would require frequent polling of the sensor and comparing any readings to a baseline. You will then need to determine what your cut off should be (ie, how fast should the object change it's motion) so that you can avoid false readings. This sensor however can be invaluable to tamper proofing an item, as almost any change shows that the object has moved and is no longer on the floor/ground.
Using alternative methods, like optical sensors, proximity sensors, etc. will allow you to measure the current distance from a reference. You can poll your reference as slow or as fast as you want, if the value changes your object has moved. This will also be much more reliable if you need to know the distance travelled, or require an event to trigger based on a distance travelled.