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.

Advertisements

8 thoughts on “A Living Position vs. Time Graph

  1. Thomas Hefner

    I have two robots on order as of today. So looking forward to their arrival soon. These robots are also cheap enough that even without grants, which is how I am able to purchase my pair, schools can afford the robots.

    Reply
  2. Tripp

    Certainly a very cool dramatization of the concept. Many of these running at once at a high speed would look cool. And the last two to stop in this case vividly show the speed difference by the end.

    Reply
  3. Elayne Grueber

    I would really appreciate a link or name of the robots. I am in the process of redesigning our physics for next year and would like to incorporate the robots into the class but I am having trouble finding them on-line. Thanks!

    Reply
    1. aphysicsmicrocosm Post author

      Hi Elayne,
      Glad to hear you’re interested in using the robots and my software. There are several teachers who are planning to use them next year, and I’m looking forward to hear about all of the ideas you all will invent to use them.

      The link to the scribbler II’s is in the top paragraph of the first few blog posts, such as this one. More details are in a comment I left at the bottom of that post. If that doesn’t answer all of your questions, please feel free to write back.

      Matt

      Reply
  4. Pingback: Modeling and Robots—on a Mac! | Quantum Progress

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s