The IEEE 802.11 standard defines the different bit rates and modulation schemes to which a WLAN device may adapt according to the channel quality. User mobility may also have an impact on the available bit rate. This paper presents a study of the bit rate evolution along time for devices that move according to the Random Waypoint mobility pattern in WLAN cells. Simulation has been applied in order to obtain statistical results that permit to characterize the evolution of the bit rate behavior along time and to compute average results in the ideal case (without interference) and in the presence of interfering devices. Our results can be useful in the solution of optimization problems in which decision on where to connect must be taken based on some minimum guaranteed bit rate. They also can be useful in the design of inter and intra-cell handover methods and load balancing schemes.