# Calculating speed the data shows that your friend

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Calculating speed The data shows that your friend took 10 seconds to run each 50-meter segment. Because the time was the same for each segment, you know her speed was the same for each segment. You can use the formula v = d / t to calculate the speed. Dividing 50 meters by 10 seconds results in a speed of 5 meters per second. Graphing the data You make a graph of the data by plotting the four points on graph paper and connecting them with a smooth line. Notice that when moving from each data point to the next, the graph goes over 10 seconds and up 50 meters. This causes the points to fall exactly in a straight line. A position vs. time graph that is a straight line always means the object moves the same distance during each time period. An object moving at a constant speed always creates a position vs. time graph that is a straight line. Figure 12.9: The data table and position vs. time graph for a runner. Runner’s Position vs. Time Position and Time Data for a Runner Time (s) Position (m) 10 0 50 100 150 20 30 Time (s) Position (m) 0 10 20 30 0 50 100 150

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254 U NIT 5 M OTION AND F ORCE Figure 12.10: A position vs. time graph for two runners. slope - the ratio of the rise (vertical change) to the run (horizontal change) of a line on a graph. Position vs. Time for Two Runners Time (s) Position (m) 25 0 100 200 300 400 500 600 50 75 100 125 150 Runner A Runner B Slope Comparing graphs You can use position vs. time graphs to compare the motion of different objects. Figure 12.10 shows the position vs. time graph for two people running along a 600-meter section of a jogging path. Both runners start at the beginning of the path (the origin) at the same time. Runner A takes 100 seconds to cover 600 meters, and runner B takes 150 seconds. Using v = d / t , runner A’s speed is 6 m/s and runner B’s speed is 4 m/s. You can see that runner A’s speed is faster by looking at the two lines on the graph. Runner A’s line is steeper. A steeper line on a position vs. time graph means a faster speed. A steeper line on a position vs. time graph means a faster speed. Calculating slope The steepness of a line is measured by finding its slope. The slope of a line is the ratio of the “rise” (vertical change) to the “run” (horizontal change). The diagram below shows you how to calculate the slope of a line. The rise is equal to the height of the triangle. The run is equal to the length along the base of the triangle. Here, the x - values represent time and the y -values represent position. The slope of a position versus time graph is therefore a distance divided by a time, which equals speed. The units for the speed are the units for the rise (meters) divided by the units for the run (seconds) or meters per second. Slope = rise 10 m run 5 s = = 2 m/s The slope of position vs.time is the speed. 10 10 5 5 0 0 Car A Position (m) Time (s) Position vs. Time Rise = 10 m Run = 5 s
255 12.3 G RAPHS OF M OTION C HAPTER 12: D ISTANCE , T IME , AND S PEED Speed vs. time graphs Constant speed on a speed vs.

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