WCYDWT?: Constant Velocity Buggies

Honors Physics is wrapping up our work with the constant velocity particle model (CVPM), which is our description of how objects move with constant velocity, including several different kinds of descriptions of motion, and lots of tools to make predictions about these kinds of motions.  We've now worked with five different representations of CVPM motion:

• x vs t graphs
• v vs t graphs
• Verbal descriptions (I called them textual descriptions in the first class today, and got the expected chorus of giggles, so I gave up on that)
• Algebraic models (equations)
• Diagrams

We worked quite a bit today with algebraic and diagrammatic representations of motion, having used graphs a great deal for the past couple of weeks.

The best way to do it is to do it, so they jumped in and formulated their own questions about the two constant velocity buggies that I gave them; I took out one battery from the red one and replaced it with a strip of copper to make it run significantly slower.  They were the equipment; the question was "what can you do with this?"

They came up with great questions - some were classics, and some were a little more out-of-the-box.  All let them test their diagramming and algebraic problem-solving chops:

• Cars facing each other - "where/when will they collide?"

• Cars starting apart - "when/where will one car pass the other?"

• Cars starting together, facing away from each other - "when will they be 10 m apart?"

Not only did they solve this one algebraically, they took their extra time and solved the problem graphically as well!

• Cars starting together - "when will one car have gone twice as far as the other?" 

This was very interesting; after a great deal of wrestling with their algebra, the time interval and the distance always canceled, leaving:

 

This is a strange result indeed - no reference to time or distance!  The interpretation: if they really do start at the same spot, the question can only be answered if the faster car has twice the speed of the slower car.  If it does, then any time or distance works.  If not, no time or distance works!