# Publication Details

 Title An elementary expression in five variables, that is relevant to many road accidents Authors Hutchinson TP Year 2021 Type Conference Paper Abstract An elementary expression in five variables, that is relevant to many road accidents This paper is relevant to the causation of a large subset of road accidents, namely, those in which a vehicle being driven forwards strikes an obstacle (such as a pedestrian, a vehicle, or a tree). In the main part of the paper, the focus is at the moment the emergency is appreciated, perhaps a couple of seconds before impact, and the question of interest is what then happens. Later in the paper, there is discussion of how to push our understanding to a point a few seconds earlier, in the hope of throwing light on accident causes. The topics within the paper are as follows. 1. A model is suggested for the relevant subset of road accidents. 2. Velocity of impact is very important in determining severity of injury. An equation for speed of impact is obtained from the model. Impact speed may be zero, meaning that impact is avoided. 3. The equation is an expression in five variables. As it is elementary, it will be of interest to educators in mathematics and other subjects, as well as to road safety specialists. 4. Two of the five variables (speed of vehicle and distance of the obstacle) are conditions existing at the initiation of the emergency; and three might approximately be called range of the sensing system, reaction time, and deceleration, and are properties of the vehicle-driver system. 5. How the emergency was generated is discussed. Why was the obstacle present? If it was because of a human error in gap acceptance, how should that error be classified? Sponsor ANZIAM: Australian and New Zealand Industrial and Applied Mathematics Conference Name 15th Engineering Mathematics and Applications Conference Conference Abbreviation EMAC 2021 Conference Location (fully online) Conference Date 2-3 December 2021

 Reference Hutchinson TP (2021) 'An elementary expression in five variables, that is relevant to many road accidents', 15th Engineering Mathematics and Applications Conference, (fully online), 2-3 December 2021.