In the situation of high intensity of motor vehicle traffic, collisions or accidents at road intersections often have the form of a collision of multiple cars. The reconstruction of such a road incident is often carried out as an attempt to estimate the velocities of individual cars, especially the velocity of the vehicle that caused the collision. In the analysis of motion of a larger number of vehicles, it may be sufficient to assume that they can be adequately represented by a system of material points with their mass values being known. In such a case, it may be possible to determine the velocity values necessary to assess the safety level and to estimate the degree of responsibility of individual drivers on the grounds of some elementary equations describing a system of material points. The objective of this article is to show, with a collision of three cars being taken as an example, that the determining of the velocity of the vehicle that caused the collision comes down to solving a few simple algebraic equations. Before the reconstruction of a road incident is commenced, data are collected from the incident site. These data constitute the basic sources of evidence. Unfortunately, they may be burdened with a wide uncertainty margin. Therefore, adequate reliability of such data is often decisive for the obtaining of a correct result of the reconstruction. The article shows a possibility of improving the reliability of such data by using relative sensitivity factors to identify the parameters of the road incident under consideration that have the strongest influence on the final calculation result. This means that the values of such parameters should be estimated with the greatest possible accuracy because they have the strongest impact on the uncertainty of assessment of the traffic situation being examined.