In traffic engineering, vehicle speed is a critical determinant of both the risk and severity of road crashes, a fact that holds particularly important for signalized intersections. Accurately selecting vehicle speeds is crucial not only for minimizing accident risks but also for ensuring the proper calculation of intergreen times, which directly influences the efficiency and safety of traffic flow. Traditionally, the design of signal programs relies on fixed speed parameters, such as the posted speed limit or the operational speed, typically represented by the 85th percentile speed from speed distribution data. Furthermore, many design guidelines allow for the selection of these critical speed values based on the designer’s own experience. However, such practices may lead to discrepancies in intergreen time calculations, potentially compromising safety and efficiency at intersections. Our research underscores the substantial variability in the speeds of passenger vehicles traveling intersections under free-flow conditions. This study encompassed numerous intersections with the highest number of accidents, using unmanned aerial vehicles to conduct surveys in three Polish cities: Toruń, Bydgoszcz, and Warsaw. The captured video footage of vehicle movements at predetermined measurement sections was analyzed to find appropriate speeds for various travel maneuvers through these sections, encompassing straight-through, left-turn, and right-turn relations. Our analysis focused on how specific infrastructure-related factors influence driver behavior. The following were evaluated: intersection type, traffic organization, approach lane width, number of lanes, longitudinal road gradient, trams or pedestrian or bicycle crossing presence, and even roadside obstacles such as buildings, barriers or trees, and others. The results reveal that these factors significantly affect drivers’ speed choices, particularly in turning maneuvers. Furthermore, it was observed that the average speeds chosen by drivers at signalized intersections did not reach the permissible speed limit of 50 km/h as established in typical Polish urban areas. A key outcome of our analysis is the recommendation for a more precise speed model that contributes to the design of signal programs, enhancing road safety, and aligning with sustainable transport development policies. Based on our statistical analyses, we propose adopting a more sophisticated model to determine actual vehicle speeds more accurately. It was proved that, using the developed model, the results of calculating the intergreen times are statistically significantly higher. This recommendation is particularly pertinent to the design of signal programs. Furthermore, by improving speed accuracy values in intergreen calculation models with a clear impact on increasing road safety, we anticipate reductions in operational costs for the transportation system, which will contribute to both economic and environmental goals.