We started today with analyzing the graphs we made from the cart on an incline plane lab to derive the kinematic equations. Although this only takes about 10-15 minutes, it made this post too long. So I made a separate post to show the process. Although most texts give these equations, many omit the entire process. For the sake of helping your students foster their connection between the graphs and the equations, Jon recommends spending the time to show these derivations. *{My guess is that you could either do this during whiteboarding, or as a mini-lecture (for those that aren’t quite ready to give up the reins, and want to be a sage on the stage again).*}

After showing all the derivations, we moved on to Lab Extension: Speeding Up and Slowing Down. {*As I’ve noted at least once before, we were given version 3 of this worksheet. However, I’m only seeing version 2 on the modeling website. I guess that’s one more reason you need to go to the workshop and not just read my blog.*}

Jon told us that he gives the students all the equipment except for the motion detector. Jon said that after the individual groups show him the completed worksheet, he provides the motion detector. After the students have all completed acquiring the data/graphs, he has them white board what they got for a given problem. Chris does it a little differently. He never gives them the detector, but rather has the students make the predictions for HW, and then the groups whiteboard their predictions at the beginning of class. He then projects the actual results after the class has come to agreement for the each given problem. {*My $0.02 on this is that I like Chris’s approach better (sorry Jon).*}

By the way, I had never seen motion maps that showed both velocity and acceleration at the same time. For those like me, you plot the velocity above the displacement vector and acceleration below. Have the points that represent the same time line up vertically. I’ve tried to show what the map for #1 would look like below:

The blue vectors represent the velocity and the red vectors represent the acceleration for an object accelerating from rest.

{*I’m honestly not sure how to draw the first point for the acceleration portion, whether they should be inline with the arrow overlapping the second point, or as shown with the first point slightly above the second. I’m guessing how I have it is correct. And no, I didn’t waste the time to make sure the arrows were to scale. Remember motion maps are qualitative, not quantitative.*}

A couple points made by Jon and Chris:

#3 is the first instance for the students where an object is speeding up even though it has a negative acceleration. You need to socratically question the students (What is happening to the magnitude of the velocity? What then is the sign of the acceleration? Can a negative acceleration increase the velocity?). According to both Chris and Jon, this is a confusing idea, since they are used to describing a negative acceleration as a deceleration (a term you should dissuade the students from using).

#4 is a similarly confusing example in that the acceleration is positive but the object is slowing down. Again, use Socratic questioning to lead the students to this idea.

#6 Jon omits this problem as changing the origin doesn’t really come up later in the curriculum. He said that it’s up to you and your students. Do you want/have time to spend on this?

{*My thoughts are that I might leave this out for standard level, buy include it for the honors level of my classes. If I have more than 6 lab groups in honors (which I did this past year (’10-’11)), I might make additional problems with the adjusted origin so each group whiteboards their own problem.*}

From there we worked on Worksheet 2, Worksheet 2a, and a supplementary worksheet.

**2a: #3**Jon mentioned that students tend to struggle with all the technical vocabulary in this problem.

**2a:#5**Chris asked the group presenting: “I remember a problem from the earlier work, where the negative velocity and it was speeding up. Why is this different?” {Your trying to get the kids to focus on the speeding up when acceleration is in the same direction as motion, (and slowing down when opposite) not based on +/- sign}

**Wkst III:**

**1 c&d**Jon mention that these problems are very tricky for students.

*I’m not sure if I would tell my students the correct value or not. I would probably just calculate the class average and then ask the students to explain our error. One side note, one of my pet peeves is “human error.” To me that is a student being lazy and not wanting to think about what they did wrong. I would push my students to say that the picket fence was rotated one way or another, photogate wasn’t level, etc.*}

*Don’t get me started on that one.*}, and a metal filing shelf (similar to this, only it was one level not two). The shelf was used over the top of the detector to help protect it from the ball. The basic procedure was to toss the ball above the motion detector and have it fall towards the detector. Again, the group with the closest value to “g” received a prize. We used the “ball toss” file provided by vernier.

*I think I might introduce video analysis at this point, either have the students do it in their groups, or run this as a demo, videotaping the students tossing the ball. Then I would show on the smartboard how to use video analysis. I would probably use the tool in LoggerPro, however, seeing Rhett Allain use VideoTracker throughout his blog, makes me think it might be worth it to have the students download and use that program*.

*However it might be worth leaving video analysis until we get to 2D motion.*}