I busted out the motion detector again today in Calculus in a last minute experiment that proved to be really good. I put the screen on the velocity vs time graph and told them to walk so that the integral of the graph was positive. One kid did that and then we examined the number and used units to figure out what it meant. With that new information, I had students walk so that the integral was….

- Equal to 1
- Equal to 1 but moving with a slower velocity
- Equal to -4
- Equal to 0
- Equal to 1 even though you moved closer to the motion detector at some point
- Equal to -2 even though you moved further away from the motion detector at some point.

It was a great way to get them to begin to understand the idea of applications of integration.

Someone walking backwards and then forward…

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This is sort of a geogebra version of the motion detector. Adjust the velocity of the object. Visible or not visible graphs of position and velocity are created as you move the object.

http://www.geogebratube.org/student/m34440

I like things like this, but the physicality of the motion detector is really crucial to me for something like this. Getting them to connect abstract ideas to physical experiences.

I much prefer a physical demonstration initially as well. Do you no if there are any smartphone apps that collect data like this and produce graphs?