Motion and Graphs: A Calculus Primer

As I have stated in the introduction to Solving Motion Problems, a moving object discussed in elementary and middle schools are usually assumed to be at a constant speed. For example, a car traveling at 65 kilometers per hour is assumed to travel at the said speed the whole time. Of course, this is not what happens in reality. The car speeds up, slows down, or stops at times.

motion graphs

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The graphs of two cars traveling at different speeds (kilometers per hour) are shown above. Car A is traveling at a  constant speed from 2:00 to 3:00 as shown in the first graph. Since the speed is constant, the graph is a horizontal line. The graph of the accelerating Car B is shown on the right. The car is accelerating, so the graph curves upward as it goes to the right. » Read more