Graphing Speed and Acceleration
Graphing Speed and Acceleration
Graphing Motion
You can show the motion of an object on a line graph in which you plot ___________________________________________________. The graphs you see in Figure 6 are distance-versus-time motion graphs. Time is shown on the horizontal axis, or ______________________. Distance is shown on the vertical axis, or __________________________________. A point on the line represents the _______________________________________________________________________. The x value of the point is time, and the y value is distance.
The steepness of a line on a graph is called _________________. The slope tells you how fast one variable _____________________________ in relation to the other variable in the graph. In other words, slope tells you the ________________
______________________________. Since speed is the rate that distance changes in relation to time, the slope of a distance-versus-time graph represents ________________. The ___________________ the slope is, the ________________
____________________________________. A ________________________________ represents motion at ______________________________________.
Calculating Slope
You can calculate the slope of a line by dividing the ________________________
__________. The rise is the _______________________________________________
___________________________________. The run is the ______________________
____________________________________________________.
Slope =
In Figure 6 using the points shown, the rise is ____________________ and the run is __________________. To find the slope, you divide _________________ by _________________. The slope is _____________________________________.
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 ___________________ 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 __________________
____________________. The horizontal line in the second segment shows that the jogger’s ________________________________________________________________.
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 _______________________. 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 _________________________________________. 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 _________________________, the graph shows you that your speed was _________________. Next, since the line is _____________________, you can tell that your acceleration was __________________________. A _______________
________________________ on a speed-versus-time graph means that the object is accelerating at _________________________________. You can find your acceleration by calculating the __________________________________. To calculate the slope, choose any two points on the line. Then, divide the ___________________________________________.
• Slope =
• Slope =
During your bike ride, you accelerated down the hill at a constant rate of ____________.
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 _____________________________________________________
______________________________. The curved line in Figure 12 tells you that during each second, you traveled a ___________________________________ 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 _______________________________________________________________________. 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 _________________
____________________________. Since the slope is increasing, you can conclude that the speed is also increasing. You are _________________________.
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