WEBVTT
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The given table shows the relation between the distance covered by a runner and a certain time.
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Determine the slope of the straight line that represents the motion of the runner.
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There are two ways of approaching this problem.
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The first way would be to draw a distance–time graph from the information in the table.
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On the 𝑥-axis, we have the time in seconds and on the 𝑦-axis the distance in meters.
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We can then plot the six points zero, zero; two, eight; four, 16; and so on, as shown on the graph.
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We can then calculate the slope or gradient of the straight line by dividing the change in the 𝑦-coordinate by the change in the 𝑥-coordinate.
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If we choose the two endpoints of the graph, we see that the change in 𝑦 is equal to 40 and the change in 𝑥 is equal to 10.
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The slope is therefore equal to 40 divided by 10.
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This is equal to four.
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We know that the slope on a distance–time graph represents speed.
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As the distance is in meters and the time is in seconds, the slope or speed will be equal to four meters per second.
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An alternate method in this question without drawing a diagram would be to recognize that the slope will be equal to the change in distance divided by the change in time.
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We could then select any two points from the table, for example, a time of two seconds and distance of eight meters and a time of eight seconds and distance of 32 meters.
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The change in distance here is equal to 32 minus eight.
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The change in time is equal to eight minus two.
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This simplifies to 24 divided by six, which once again is equal to four meters per second.