# Building the Constant Acceleration Particle Model (New Paradigm Investigation)

In my Physics 10 update/upgrades, I built a new paradigm investigation for the Constant Acceleration Particle Model. The activity described here gets at the same things as my older activity, but it allows groups to do the investigation rather than the entire class together, and it gives more structure and space to the discussion. The students do more of the talking (and more of the students do talk) in this version, too.

Before this model, we have done Constant Velocity, Balanced Forces, and an introduction to Center of Mass.

In my Balanced Forces unit, students have practice thinking about and drawing qualitative velocity-time graphs when objects are speeding up and slowing down, so they have been primed for this work and discussion already.

### Fan Carts and Motion Sensors

This activity starts off the unit. Students have already seen fan carts, so the “Hey, I want to show you something (relatively) cool” moment is to show them the motion detector.

We gather around a lab table. I have a student bring up their computer and set up Logger Pro. I show them the motion detector. Get everyone to be quiet enough to hear it click when we turn it on. We get to talk for a moment about what it is doing, then I show them how it makes the position-time graph. We move the cart back and forth in front of the sensor to get our bearings with how it all comes together.

I had out the packets, and they open them to the first inside page—the fan cart investigation.

At this point, they are set to do the first part of the page in groups, but it saves some time to have them talk for a minute about how to get a fan cart to slow down. At this point in the year, a lot of them still have a strong idea (whether they realize it or not) that everything starts from rest, so it isn’t very obvious to them how you could get one to be slowing down. A frequent suggestion is to “put your hand in front of it”. It only takes a moment to show them that if the cart is already moving, the fan can slow it down (depending on the direction it is facing).

Although the page only asks them to do slowing down once, since it doesn’t specify the direction, both directions will usually show up in the work among the different groups. That little bit of ambiguity adds to the discussion, and helps students focus (during the discussion) on the difference between how the velocity-time graph shows the direction of motion and how it shows speeding up versus slowing down.

The groups spread out and work through the three situations. Learning to use the motion sensors well takes a little coaching from me. As I move around to different groups, I help them identify which part of the graph shows the motion they wanted to capture and encourage them to sketch only that part on their papers.

### Board Meeting and Discussion

After capturing graphs for the three situations, groups make whiteboards of the top portion of the page.

Once they have put the graphs on the boards, the class circles up for a board meeting. The first order of business is to come to an agreement on what the graphs looked like. They move to translate the bits of messiness from the real graphs into simpler shapes that show the essence of what they captured. Their goal is to come to a consensus about the 6 graphs. As they listen to questions and comments from their peers, they update their boards to show their thinking. Sometimes they look back at their computers to check a graph. It’s easy enough to quickly run one again if we are having trouble coming to agreement. Was the line straight or was it a curve? Which way did the curve go? Were you drawing the graph just for when the cart was speeding up, or did you also draw the part when your hand stopped it? It takes a few minutes to get all of the whiteboards updated, but they can handle that discussion mostly on their own.

The next phase of their discussion is centered around the questions at the bottom of the page (as well as in the top right-hand corner of the page). Their new goal is to come to a consensus about what information about an object’s motion they can learn from a velocity-time graph. In this part, they are able to lead most of the discussion themselves, but I throw questions into the mix, too. By the end, they are in agreement about how to tell the direction of motion, whether an object is speeding up or slowing down, and what the graph looks like when the object is changing directions.

The last step is to see what we can say so far about the slope of the velocity-time graph. What would it mean if the graph were steeper? That part is easier—and we come to agreement pretty quickly that a steeper graph could mean, for example, that the object is speeding up more quickly (maybe the fan is set to a higher setting). The tough part is—what does the sign of the slope mean? They talk about it a bit, but come to realize that they aren’t quite sure what it means. Not yet. I don’t let them get stuck in this discussion for too long. We set that part of the question aside as something we can investigate later. This is only page 2 of a brand new packet, after all.

Finally, I ask them if they’d like to know the name that physicists give to the slope on the velocity-time graph. We define acceleration as the slope on the velocity-time graph—a definition that will be a helpful way of thinking about acceleration for some time to come.

The next day, we follow up on our ideas about the shapes of these graphs and the meanings of the features by doing a Walk-A-Graph activity where students practice being the object for a variety of x-t and v-t graphs.

This model-building class activity fits well with Modeling Instruction pedagogy, and it is shared under a free and open copyright. Please feel free to use, modify, share, etc—as long as you follow the Creative Commons license on this page. Let me know if you try this with your students!