An Exercise in Vehicle Kinematics and Energetics

We physics teachers are forever in search of real-life applications of the theoretical concepts we teach. In mechanics we often utilize vehicle motion exercises, yet most textbook problems involving these are rather tame and deal with constant acceleration. What often captures the imagination of students is the actual performance of cars they drive: times for accelerating from zero to 100 km/h, top speed, energy consumption, power, and so on. Such data, of major concern to car designers and salesmen, are now readily available on the Internet and in magazines such as "Car & Driver" and "Road & Track" for a wide spectrum of vehicles. Their use in the classroom has been recommended in several articles that appeared in this journal. When reporting acceleration of vehicles, the first (high-acceleration) stage, as the engine "revs up" to its full power, is usually omitted. A glance at a typical velocity-versus-time curve (Fig. 1, for a MINI Cooper S; these data are also used in Figs. 3 and 5) shows that as the velocity increases toward the maximum attainable speed in a finite time, the acceleration decreases. Thus, overtaking a car at high speeds takes much longer than the initial acceleration might suggest--this is most unlike a constant acceleration scenario.