In kinematics we often compare position/time graphs with velocity/time graphs.  The key feature to remember is that the velocity/time graph will always represent the SLOPE of the position/time graph over any interval.

To successfully convert these position/time graphs below into a velocity/time graph, your first step should be to calculate the slope (rise/run) in each interval.

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Below you can find a video which works through a similar problem if you wanted to see an example before trying them on your own.

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If you were able to successfully convert the graphs above, increase the difficulty by introducing quadratic position/time graphs.  Remember that IF the position/time graph is a quadratic, you know that the velocity/time graph will be linear!

You can also help yourself in drawing the velocity/time graph by remembering that the vertex of the parabola of the position/time graph is going to be the x-intercept of the velocity/time graph.

The final hint for solving these types of problems, is remembering that you can actually break a parabola up into a bunch of small straight lines and by using those estimates to draw your velocity/time graph, you will get a remarkably close answer.

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Now it’s time to try starting with a velocity/time graph and then converting to a position/time graph.  Feel free to check out the example video below first before trying some on your own.  Remember that the velocity/time graph represents the slope of the position/time graph.

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These final questions are the extra special challenge questions!  There is a video below that shows how to deal with a velocity/time graph once a slope is introduced.  Remember that the velocity/time graph represents the slope of the position/time graph.

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