5 A Mathematical Model Of Motion Answers

Once we are done discussing yesterday's checkpoint, we move to discussing and focusing on the mathematical model. I use the checkpoint as something to base our next discussion on. I write the notes on the board and ask the students write these ideas in their notebooks throughout our discussion. I have students participate in the discussion as I reveal the mathematical models and like to have students write these concepts down as notes for them to use as a reference.

Students start by stating what are 3 ways we could define velocity from what we already know or the reading from the textbook the night before. After multiple students volunteer, the list contains the three following definitions: slope of a position vs. time graph, change in position during a time interval, and speed in a given direction (or speed + direction). I ask them if they think that velocity and speed are the same thing and I get mixed answers, but I usually have a student that says that direction is the main difference.

The goal is to have students focus on the mathematical model and where it comes from. I have students think back to the checkpoint and to the Dune Buggy Lab and what the position vs. time graph looked like. I draw a line with a positive slope as a reminder. From there, we review the mathematical model that we came up with which is: final position = velocity x time + initial position. After we select letters to represent position, velocity and time, I write the equation in symbols and make sure to emphasize that the f and i are to distinguish between the final and initial positions. Then I go through the how to rearrange the equations as in the Constant Velocity Mathematical Model Notes. I show them a circle of how to easily rearrange the equation similar to the idea below:

Finally I ask them if we use the same equation for speed. When they say no, I ask them if they saw one in the reading and they typically come up with the equation: average speed = total distance/time. I tell them that it is similar to the velocity equation, the only difference being that velocity has a direction so it could be positive or negative and speed does not have a direction so it has no sign. By the end of this section of a lesson, students notes should look like the Constant Velocity Mathematical Model Notes, which they can use to help them in the next part of the lesson.