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In this paper, we present a real-time algorithm for automatic recognition of not only physical activities, but also, in some cases, their intensities, using five triaxial wireless accelerometers and a wireless heart rate monitor. The algorithm has been evaluated using datasets consisting of 30 physical gymnasium activities collected from a total of 21 people at two different labs. On these activities, we have obtained a recognition accuracy performance of 94.6% using subject-dependent training and 56.3% using subject-independent training. The addition of heart rate data improves subject-dependent recognition accuracy only by 1.2% and subject-independent recognition only by 2.1%. When recognizing activity type without differentiating intensity levels, we obtain a subject-independent performance of 80.6%. We discuss why heart rate data has such little discriminatory power.