A boy moves along a straight line. On the graph, the blue line shows the displacement 𝑑 of the boy from his starting position over time 𝑡. What is his speed two seconds after he starts walking?
The graph we’re given shows displacement in meters on the vertical axis and time in seconds along the horizontal axis. Recall how to find speed from a displacement–time graph. Speed is the magnitude or size of the slope of the displacement–time graph. So let’s find the boy two seconds after he starts walking. 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. This section here from zero seconds until four seconds is a straight line, which means he has constant speed for this whole segment. So what we need to find is the slope of this line segment.
Now recall how to find the slope of a line. The slope is the vertical difference divided by the horizontal difference between any two points on the line. So let’s take the start and endpoints of the line, first of all, at zero, zero and then at four, four. We take the coordinates of the second point minus the coordinates of the first point. So the vertical difference between these points is four minus zero and the horizontal difference is also four minus zero. And four minus zero just gives us four. So the slope is four divided by four, which is equal to one.
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. So this gives us our answer that the boy’s speed two seconds after he starts walking is one meter per second.
Part two of this question asks, “What is his speed six seconds after he starts walking?” So we can do the same thing, first of all, finding six seconds on the horizontal axis. And we find this falls in the middle of this segment, which is a straight line from four seconds until eight seconds. Straight line meaning that the boy is moving with a constant speed. So we just need to find the slope of the line between these two points.
So again, we need to find the coordinates of the beginning and end of this line. So we have at the beginning here the point four, four and then, at the end, the point eight, five. 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. Five minus four gives us one, and eight minus four gives us four. One divided by four is a quarter or 0.25. 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.
And this gives us the answer that the boy’s speed six seconds after he starts walking is 0.25 meters per second.