WEBVTT
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A boy moves along a straight line.
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On the graph, the blue line shows the displacement đť‘‘ of the boy from his starting position over time đť‘ˇ.
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What is his speed two seconds after he starts walking?
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The graph weâ€™re given shows displacement in meters on the vertical axis and time in seconds along the horizontal axis.
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Recall how to find speed from a displacementâ€“time graph.
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Speed is the magnitude or size of the slope of the displacementâ€“time graph.
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So letâ€™s find the boy two seconds after he starts walking.
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He starts walking at a time of zero seconds and then two seconds later is at two seconds on the horizontal axis, at which point he is here.
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This section here from zero seconds until four seconds is a straight line, which means he has constant speed for this whole segment.
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So what we need to find is the slope of this line segment.
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Now recall how to find the slope of a line.
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The slope is the vertical difference divided by the horizontal difference between any two points on the line.
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So letâ€™s take the start and endpoints of the line, first of all, at zero, zero and then at four, four.
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We take the coordinates of the second point minus the coordinates of the first point.
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So the vertical difference between these points is four minus zero and the horizontal difference is also four minus zero.
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And four minus zero just gives us four.
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So the slope is four divided by four, which is equal to one.
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And for the units, we need the units of the vertical axis, which are meters, divided by the units of the horizontal axis, which are seconds.
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So this gives us our answer that the boyâ€™s speed two seconds after he starts walking is one meter per second.
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Part two of this question asks, â€śWhat is his speed six seconds after he starts walking?â€ť
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So we can do the same thing, first of all, finding six seconds on the horizontal axis.
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And we find this falls in the middle of this segment, which is a straight line from four seconds until eight seconds.
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Straight line meaning that the boy is moving with a constant speed.
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So we just need to find the slope of the line between these two points.
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So again, we need to find the coordinates of the beginning and end of this line.
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So we have at the beginning here the point four, four and then, at the end, the point eight, five.
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And then to find the slope, we need the vertical difference between those two points, which is five minus four, divided by the horizontal difference, which is eight minus four.
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Five minus four gives us one, and eight minus four gives us four.
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One divided by four is a quarter or 0.25.
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And for the units, we take the units of the vertical axis, which are meters, divided by the units of the horizontal axis, which are seconds.
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And this gives us the answer that the boyâ€™s speed six seconds after he starts walking is 0.25 meters per second.