## 8 (d) Distance Versus Time Graph

Graphing Motion

You can show the motion of an object on a line graph in which you plot distance versus time. The graphs you see in Figure 6 are distance-versus-time motion graphs. Time is shown on the horizontal axis, or x-axis. Distance is shown on the vertical axis, or y-axis. A point on the line represents the distance an object has traveled at a particular time. The x value of the point is time, and the y value is distance.

The steepness of a line on a graph is called slope. The slope tells you how fast one variable changes in relation to the other variable in the graph. In other words, slope tells you the rate of change. Since speed is the rate that distance changes in relation to time, the slope of a distance-versus-time graph represents speed. The steeper the slope is, the greater the speed. A constant slope represents motion at constant speed.

Calculating Slope

You can calculate the slope of a line by dividing the rise by the run. The rise is the vertical difference between any two points on the line. The run is the horizontal difference between the same two points.

In Figure 6 using the points shown, the rise is 400 meters and the run is 2 minutes. To find the slope, you divide 400 meters by 2 minutes. The slope is 200 meters per minute.

Different Slopes

Most moving objects do not travel at a constant speed. The graph shows a jogger’s motion on her second day. The line is divided into three segments. The slope of each segment is different. From the steepness of the slopes you can tell that the jogger ran the fastest during the third segment. The horizontal line in the second segment shows that the jogger’s distance did not change at all.

You can show the motion of an object on a line graph in which you plot distance versus time. The graphs you see in Figure 6 are distance-versus-time motion graphs. Time is shown on the horizontal axis, or x-axis. Distance is shown on the vertical axis, or y-axis. A point on the line represents the distance an object has traveled at a particular time. The x value of the point is time, and the y value is distance.

The steepness of a line on a graph is called slope. The slope tells you how fast one variable changes in relation to the other variable in the graph. In other words, slope tells you the rate of change. Since speed is the rate that distance changes in relation to time, the slope of a distance-versus-time graph represents speed. The steeper the slope is, the greater the speed. A constant slope represents motion at constant speed.

Calculating Slope

You can calculate the slope of a line by dividing the rise by the run. The rise is the vertical difference between any two points on the line. The run is the horizontal difference between the same two points.

In Figure 6 using the points shown, the rise is 400 meters and the run is 2 minutes. To find the slope, you divide 400 meters by 2 minutes. The slope is 200 meters per minute.

Different Slopes

Most moving objects do not travel at a constant speed. The graph shows a jogger’s motion on her second day. The line is divided into three segments. The slope of each segment is different. From the steepness of the slopes you can tell that the jogger ran the fastest during the third segment. The horizontal line in the second segment shows that the jogger’s distance did not change at all.