The course of the braking process is critical for the safety of road traffic. The importance of all the factors that can affect the vehicle stopping distance becomes particularly conspicuous in critical situations. The braking process may be analysed in terms of its mechanics, especially the contact forces and the dynamics of the working parts of the braking system; on the other hand, it may also be examined from the point of view of psychophysical factors. The latter aspect begins to be noticed when the stress-induced factors caused by activities of military nature are taken into account. In the article, the authors have analysed the factors that affect the driver’s perception time and the impact of this time on the vehicle braking distance as a function of vehicle speed. Analytical calculation results have also been presented to illustrate the relationships governing this process and to show the influence of changes in the stopping time on the vehicle stopping distance. In consideration of special vehicles used in military missions, some additional factors that might affect the time of risk have been highlighted. The said factors have been tabulated in accordance with the hierarchy of their occurrence. Some discrepancies noticed in the literature data published over the years and concerning the stopping time have also been pointed out.