Distance-Time Graphs Accelerated motion is represented by a curved line on a distance-time graph. In a nonlinear graph, a curve connects the data points that are plotted. Figure 18 is a distance-time graph. The data in this graph are for a ball dropped from rest toward the ground.

Compare the slope of the curve during the first second to the slope of the curve during the fourth second. Notice that the slope is much greater during the fourth second than it is during the first second. Because the slope represents the speed of the ball, an increasing slope means that the speed is increasing. An increasing speed means that the ball is accelerating.

Figure 18 A distance-time graph of accelerated motion is a curve.

d

Instantaneous Acceleration

Acceleration is rarely constant, and motion is rarely in a straight line. A skateboarder moving along a half-pipe changes speed and direction. As a result, her acceleration changes. At each moment she is accelerating, but her instantaneous acceleration is always changing. Instantaneous acceleration is how fast a velocity is changing at a specific instant.

Acceleration involves a change in velocity or direction or both, so the vector of the skateboarder's acceleration can point in any direction. The vector's length depends on how fast she is changing her velocity. At every moment she has an instantaneous acceleration, even if she is standing still and the acceleration vector is zero.

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