This paper evaluates the performance of the Routing Protocol for Low power and lossy networks (RPL) under mobility in vehicular ad hoc networks (VANETs). It shows that fine-tuning RPL's timers, including using an immediate response to topology changes and an adaptive timer approach, can improve packet delivery ratio by up to 20% compared to the standard RPL implementation. Simulation results demonstrate that decreasing the DIO message period and ETX probe period improves delivery ratio, but also increases overhead. An adaptive timer approach is recommended to balance performance and overhead with changing network conditions.