Physical activity classification is crucial for the design of novel context aware services. The aim of this short paper is to devise a method for the classification of normal activities of a subject during his daily living from the accelerations of the body center of gravity. We will specifically address the detection of displacement-related activities, such as walking or running. We will also address whether particular details of the activity such as the inclination of the surface or the existence of staircases can be detected from the signals. Initial experimental results are given.