A Living Position vs. Time Graph

I originally set up this exercise to demonstrate squared vs. linear scaling rules long after my kinematics units were done.  I was going to just program a constant velocity and constant acceleration robot, and run them side-by-side for 1 second, 2 seconds, etc. with discussion in between.  Then I though it would be easier to program several robots with the set times and just swap out robots.  When that was done, I realized i could run them all at the same time, and low and behold they created a living position vs. time graph!  This will definitely be my introduction to position vs. time graphs for accelerated motion next year.

As you can see, the constant velocity robot’s distance doubles when time doubles and  triples when time triples, while the constant acceleration robot’s distance quadruples when time doubles and “nine-tuples” when time triples, creating an easy to see demonstration of the scaling rules.  It’s also a nice display of the accuracy of the robots.  I set both robots to travel one foot (one square of tile) in the first second.  The accelerated robot stops less than a cm from the ninth tile and all the rest are at least as accurate.  I think the value as an introduction to the position vs. time graph for accelerated motion is obvious, and this could be repeated for comparison with a robot that slows down or one that starts with an initial velocity and then speeds up.  Students often have difficulty seeing differences in the different curved graphs, which can be very subtle for them at first glance.