Smart phone platforms, equipped with a rich set of sensors enable mobile sensing applications that support users for both personal sensing and large-scale community sensing. In such mobile sensing applications, the position/placement of the phone relative to the user body provides valuable context information. For example, in physical activity recognition using motion sensors, the position of the phone provides important information, since the sensors generate different signals when the phone is carried in different positions and this makes it difficult to successfully identify the activities with sensor data coming from different positions. In this paper, we investigate whether it is possible to successfully identify phone positions using only accelerometer data which is the most commonly used sensor on physical activity recognition studies, rather than using additional sensors. Additionally, we explore how much this position information increases the activity recognition accuracy compared with position independent activity recognition. For this purpose, we collected activity data from 15 participants carrying three phones in different positions, performing activities of walking, running, sitting, standing, climbing up/down stairs, transportation with a bus, making a phone call, interacting with an application on the smart phone, sending an SMS. The collected data is processed with the Random Forest classifier. According to the results of position recognition, using basic accelerometer features which are also used in the activity recognition, can achieve an accuracy of 77.34%, however, this ratio increases to 85% when basic features are combined with angular features calculated from the orientation of the phone. According to the results of the activity recognition experiments, on average the results are similar for position specific and position independent recognition. Only for the pocket case, 2% increase was observed.