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We find the velocity graph very easily simply by calculating the slope of every increment within the distance/time graph.

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We know we were going at a constant rate because in Minecraft mine carts on powered rails consistently travel at the same speed. Because the mine cart track stays powered throughout and is in a straight line we know that we are travelling at a constant rate. We can also see that we are travelling exactly straight as the y and z axes are changing.

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Constant rate of change (extra challenge 😈)

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Constant rate of change (extra challenge 😈)

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We can tell where the speed is highest and lowest simply by looking at the slope. The slope at any given increment is the velocity within that increment (slope is y/x, in these examples y is distance and x is time. Speed is distance over time so therefore the slope in this example is velocity). So we can see that the speed is lowest in the last few seconds and the speed is fastest in the increment in between 16 and 17 seconds. We know this because in the last few seconds the slope is the lowest and in the increment between 16 and 17

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This works because the slope itself is a representation of the velocity of the object (Minecraft Nate). In the first second of the graph the y value changes from 0 to 3. Thus the velocity within this period was 3 m/s. But also we can observe that the slope during this period was 3/1. Thus, the slope represents the velocity of the graph which allows us to say the change in slope is the acceleration.

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Within a distance over time graph, the change in slope between increments of the graph tells you the acceleration of the data For example, above, we can see that the slope changes from 3 to 2 in between the first and second increment. This tells us that the acceleration between these increments is -1.