Reconfigurable intelligent surfaces (RISs) have attracted significant attention due to their capability in customizing wireless communication environments to improve system performance. In this study, we investigate the performance of an RIS-assisted multi-user multiple-input single-output wireless communication system, considering the impact of channel aging caused by users’ relative movements. In particular, first, we propose a model incorporating the joint effects of channel aging and channel estimation errors to investigate the performance of the RIS-assisted system. Then, we derive novel closed-form expressions for characterizing the sum spectral efficiency with zero-forcing precoding. From our analysis, we unveil that an increase in the temporal channel correlation coefficient, the number of base station antennas, and the received power at the users could help improve system performance. Furthermore, increasing the number of reflecting elements M of the RIS generally yields a good system performance, but with a diminishing return when M is sufficiently large. Finally, simulation results are presented to validate the accuracy of the analytical results.