Ingeniería Investigación y Tecnología, volumen XVI (número 3), julio-septiembre 2015: 391-405 ISSN 1405-7743 FI-UNAM (artículo arbitrado) Modelado de la velocidad en curvas y el comportamiento en seguimiento de coche de vehículos autónomos en un mundo virtualAbstract This article deals with mathematical models for controlling vehicles behavior in a virtual world, where two behaviors are considered: 1) curve turning and 2) car following situations, in this last is essential to provide a safety distance between the leader and the follower and at the same time keep the follower not delayed with respect to the leader, and in a curve turning the complexity is to provide a safety speed inside the curve and keep the car inside the lane. Using basic information as vehicles position, mathematical models can be developed for explaining the heading angle and the autonomous vehicles speed on curves, i.e. the controlled by the models. A model that predicts the autonomous vehicle speed on curves is developed considering previous data in other curves. Two models that control the acceleration/deceleration behavior of autonomous vehicles in a car following a proposed algorithm which enables accuracy in order to imitate the human behavior for accelerating and braking, and the second model provides a safety distance between the follower and the leader at sudden stops of the the leader car similar to the human behavior. Ingeniería Investigación y Tecnología, volumen XVI (número 3), julio-septiembre 2015: 391-405 ISSN 1405-7743 FI-UNAM 392