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Prior research on intelligent reflection surface (IRS)-assisted unmanned aerial vehicle (UAV) communications has focused on a fixed location for the IRS or mounted on a UAV. The assumption that the IRS is located at a fixed position will prohibit mobile users from maximizing many wireless network benefits, such as data rate and coverage. Furthermore, assuming that the IRS is placed on a UAV is impractical for various reasons, including the IRS's weight and size and the speed of wind in severe weather. Unlike previous studies, this study assumes a single UAV and an IRS mounted on a mobile ground vehicle (M-IRS) to be deployed in an Internet-of-Things (IoT) 6G wireless network to maximize the average data rate. Such a methodology for providing wireless coverage using an M-IRS assisted UAV system is expected in smart cities. In this paper, we formulate an optimization problem to find an efficient trajectory for the UAV, an efficient path for the M-IRS, and users' power allocation coefficients that maximize the average data rate for mobile ground users. Due to its intractability, we propose efficient techniques that can help in finding the solution to the optimization problem. First, we show that our dynamic power allocation technique outperforms the fixed power allocation technique in terms of network average sum rate. Then we employ the individual movement model (Random Waypoint Model) in order to represent the users' movements inside the coverage area. Finally, we propose an efficient approach using a Genetic Algorithm (GA) for finding an efficient trajectory for the UAV, and an efficient path for the M-IRS to provide wireless connectivity for mobile users during their movement. We demonstrate through simulations that our methodology can enhance the average data rate by 15\% on average compared with the static IRS and by 25\% on average compared without the IRS system.