Students will be able to write a mathematical model to describe uniform acceleration from a position vs. time graph and a velocity vs. time graph and use them to solve problems for velocity, time, acceleration and displacement.

Relationships between position and time and between velocity and time allow students to solve for acceleration.

The goal of this lesson is to define acceleration in terms of velocity and to develop the mathematical model in a way that students can use it to solve problems for acceleration, velocity, time and displacement. I like to focus on the graphs and multiple representations before determining the equations to use in this unit because the students can see where the equations are coming from. In this lesson, students develop mathematical models to supplement the graphical and written models they have from the previous lesson to help them calculate numerical answers.

10 minutes

Since this lesson comes at the beginning of the week, I start out class with Physics Family time. I like to do this base group time to help build peer-to-peer relationships in my classroom as well as a sense of community and a positive learning environment for students. The activity I selected for this lesson is a rock paper scissors competition. I like doing this activity because it is something that any student can be good at regardless of academics or social status because it is really based on luck.

The way I run my competition is that I have each Physics Family pick a representative that will compete on their Physics Family's behalf. I set up a bracket on the board like a sports bracket and put the teams on the board. Each round two members, each from a different group, compete in the best of three until the last round when we have a winner. I like this activity because students encourage their teammates. Since we work in groups a lot in my classroom, I like to promote positive interactions between students.

10 minutes

After Physics Family time, I ask students to go back to their assigned seats and take out their packets opening to Worksheet #2 Interpreting Graphs of Accelerated Motion. Since they finished it in class the day before, I go over the WS #2 KEY using the document camera in my classroom which projects the image of my worksheet on the front projector screen. I ask students to raise their hand to answer questions and try to get a different student to answer each question.

The first problem has them looking at what is happening to the slope at each point. When students have questions about this problem, I tell them that the best way to look at it is if they draw their slope lines in and see if the slope is getting steeper or less steep. The second problem gives a quantitative velocity vs. time graph that guides them to identify the different parts of the mathematical model like slope (acceleration) and y-intercept (initial velocity).

20 minutes

After we go over Worksheet #2, I ask students to find their Cell Phone Speed Dial Partner #5 to work with on the Rally Coach Uniform Acceleration. Since we have done a Rally Coach activity before, I just ask students to remind me how they go about completing their problems. They tell me each student will be in charge of writing the answers for each problem in their column. Both partners will be getting the same grade so to ensure that they agree with what their partner wrote, they must check their partner's work and come to a consensus before they hand it in.

I remind students that these are velocity vs. time graphs and if the object is accelerating or decelerating the graphs should have a positive or negative slope, not horizontal lines or curved lines. After the initial instructions I give students about 20 minutes to work, reminding them that both partners are receiving the same grade.

20 minutes

After the rally coach activity, I want to introduce students to the mathematical models and equations that we will be using throughout the rest of the unit. To do that I lead a mini-lesson up at the board to develop mathematical models from the graphs they saw in the Motion on an Incline Lab and use those as equations. The full Uniform Acceleration Calculation Notes are seen here; my hope is that students are taking notes and that their notes are similar to mine by the end of the mini-lesson.

The way I start out this mini-lesson is to ask students to remember back to the Motion on an Incline Lab and I ask them what they remember about the position vs. time and velocity vs. time graphs. After those are up on the board, we use the shapes to lead us to the general equation for each graph and then to the mathematical model for each graph, which I talk about in Prior Knowledge from Motion on an Incline Lab. After we develop the mathematical models, I go through how to change these into more friendly symbols for us to use in equations as we solve problems, which I discuss in Mathematical Model into Equations. The students know what most of the symbols are for position, velocity, acceleration and time so I ask them to help me make the equations as I write on the board. Finally, we go through two example problems using the equations, which I discuss in Example Problems.

10 minutes

To practice what they learned from their reading and the uniform acceleration notes that they just took, I have students work on Worksheet #3 Uniform Acceleration Calculations. There are 8 questions that ask students to solve for different variables. Problems are also at varying levels of difficulty, so some questions should be easy and some should be more challenging for students.

I ask students to use the remainder of the period to work on these problems and finish problems #1, 2, and 3. Whatever they don't finish is homework. I ask them to chose a partner that is not at their table to work with to complete the 3 problems; this way they can compare answers during the next lesson. I have students work with a partner on these problems because it is the first time they are using the equations as models instead of the graphs to understanding accelerated motion. While students are working, I walk around to make sure that students are on task and showing their work properly.