Movement is very important for humans. From our earliest days, we seem eager to get up and move around. The most celebrated moments of a child’s life seem to be geared around the ability to move: the first crawl, the first walk, the first bike ride, and (every parent’s nightmare) the first driver’s license. The ability to get around is one of the most cherished abilities and freedoms. For many Americans, our ability to get around when and how we want is almost considered a sacred right. Physics textbooks, which have many chapters devoted to motion, build a great many examples and problems around our means of propulsion. We model displacement problems on people walking in different directions along city blocks. We work constant acceleration problems that deal with dragsters speeding down a track. We study the issue of relative velocities with problems of airplanes flying in crosswinds. Even when we discuss relativity, we start it by considering motion on a train. However, rarely do we ever investigate the motion of these objects very closely. In most problems and examples, we assume that the motion occurs either as constant velocity or constant acceleration. This is hardly ever the case. Due to factors like friction, wind resistance, or even the manner in which the propulsion occurs, motion often involves complicated accelerations both in the positive and negative directions that cause the velocity to change on a constant basis.
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