This paper addresses an unfairness problem that exists among vehicles of distinct velocities in IEEE 802.11p based vehicle-to-infrastructure (V2I) networks used for drive-thru Internet applications. The standard IEEE 802.11p does not take into account, the residence time of vehicles within the coverage of each road side unit (RSU), for granting channel access. Due to this, a vehicle moving with higher velocity has less chance to communicate with the RSU, as compared to vehicles with lower velocity, due to its shorter residence time in the coverage area of RSU. Accordingly, the data transfer performance of a higher velocity vehicle gets degraded significantly, as compared to that of the vehicle with lower velocity, resulting in unfairness among them. In this paper, our aim is to resolve this unfairness problem by assigning the transmission opportunity (TXOP) limits to vehicles according to their mean velocities. Using an analytical model, we prove that tuning TXOP limit proportional to mean velocity can ensure fairness among vehicles belonging to distinct classes of mean velocities, in the sense of equal chance of communicating with RSU. Analytical results are validated using extensive simulations.