## 9 (d.a.) DVT and VVT graphs

**Graphing Acceleration**

Suppose you ride your bicycle down a long, steep hill. At the top of the hill your speed is 0 m/s. As you start down the hill, your speed increases. Each second, you move at a greater speed and travel a greater distance than the second before. During the five seconds it takes you to reach the bottom of the hill, you are an accelerating object.

__You can use both a speed-versus-time graph and a distance-versus-time graph to analyze the motion of an accelerating object.__

__Speed-Versus-Time Graph__

Figure 11 shows a speed-versus-time graph for your bicycle ride down the hill. What can you learn about your motion by analyzing this graph? First, since the line slants upward, the graph shows you that your speed was increasing. Next, since the line is straight, you can tell that your acceleration was constant. A slanted, straight line on a speed-versus-time graph means that the object is accelerating at a constant rate. You can find your acceleration by calculating the slope of the line.

Distance-Versus-Time Graph

You can represent the motion of an accelerating object with a distance-versus-time graph. Figure 12 shows a distance-versus-time graph for your bike ride. On this type of graph, a curved line means that the object is accelerating. The curved line in Figure 12 tells you that during each second, you traveled a greater distance than the second before. For example, you traveled a greater distance during the third second than you did during the first second.

The curved line in Figure 12 also tells you that during each second your speed is greater than the second before. Recall that the slope of a distance-versus-time graph is the speed of an object. From second to second, the slope of the line in Figure 12 gets steeper and steeper. Since the slope is increasing, you can conclude that the speed is also increasing. You are accelerating.

What does a curve line on a distance versus time graph tell you?