Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information.... 
Home Newtonian Physics Acceleration and Free Fall Varying Acceleration  
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Varying AccelerationSo far we have only been discussing examples of motion for which the vt graph is linear. If we wish to generalize our definition to vt graphs that are more complex curves, the best way to proceed is similar to how we defined velocity for curved xt graphs:
In the skydiver example, the xt graph was not even used in the solution of the problem, since the definition of acceleration refers to the slope of the vt graph. It is possible, however, to interpret an xt graph to find out something about the acceleration. An object with zero acceleration, i.e., constant velocity, has an xt graph that is a straight line. A straight line has no curvature. A change in velocity requires a change in the slope of the xt graph, which means that it is a curve rather than a line. Thus acceleration relates to the curvature of the xt graph. Figure m shows some examples. In the example 6, the xt graph was more strongly curved at the beginning, and became nearly straight at the end. If the xt graph is nearly straight, then its slope, the velocity, is nearly constant, and the acceleration is therefore small. We can thus interpret the acceleration as representing the curvature of the xt graph, as shown in figure m. If the "cup" of the curve points up, the acceleration is positive, and if it points down, the acceleration is negative.
Since the relationship between a and v is analogous to the relationship between v and x, we can also make graphs of acceleration as a function of time, as shown in figure n.
→ Solved problem: Drawing a vt graph. page 125, problem 14 → Solved problem: Drawing vt and at graphs. page 126, problem 20
Figure o summarizes the relationships among the three types of graphs. Discussion Questions


Home Newtonian Physics Acceleration and Free Fall Varying Acceleration 