Dashboard Calculus

It would be a shame for Calculus students to get behind the wheel of a car and not even realize that their favorite subject is being displayed right there on the dashboard. The speedometer represents your velocity function while the odometer represents your "distance traveled" function. In this construction, press "start," drag the speedometer needle, and examine how distance traveled may be viewed as the "area under the velocity curve." Use "guess average" to intuitively predict what might be considered the average velocity over the time interval. Use the "actual average" slider to show what the true average velocity is over the time interval. If construction runs poorly inside a web browser, consider downloading the GeoGebra file and opening in the standalone app.