We just finished our unit on constant velocity motion and this is the first day of the new unit on Uniform Acceleration; I begin with a paradigm lab in which students examine the motion of a cart on an incline. The goal of this lesson is for students to participate in a structured inquiry lab and to determine how position, velocity and time impact acceleration. They will collect and use data and graphs from a cart moving down an inclined plane.
To start the pre-lab discussion, I provide students with a visual example of accelerated motion at the beginning of the lab. I let a cart roll down an inclined track and ask students for observations about the cart's motion. As students raise their hands to provide answers, I record all observations on the board. If students say that the cart accelerates, I tell them that we will wait to use this term until we have formally defined it; I ask for simpler way to describe the motion, namely, that the cart is speeding up.
After there observations have all been written on the board, I ask which of these observations are measurable and I start a new list. This list contains any measurable quantity that students come up with. Eventually students will come up with the most important quantities: the time, position and speed or velocity. Since I ask students to come up with a tool that they can use to measure the quantities, they usually tell me that a radar gun can be used to measure speed directly. Unfortunately, we do not have any radar guns at school so we cannot measure speed directly. Instead, I tell them that they can measure position and time. This should be deja vu for many students, as I we have had the same discussion in the Dune Buggy Lab in the constant velocity unit.
After we agree that position and time are the variables that we will be focusing on, I have them decide which should be the independent variable and which should be the dependent variable. Similar to the Dune Buggy Lab, they may say either of them could be the independent variable and that is true. I remind them, however, of what graphs we saw last unit and I ask: Have you ever seen a Time vs. Position graph? They respond no and decide that time should be the independent variable and position should be the dependent variable. We also discuss that the remaining variables that are on the board are things that we will want to keep constant so we can get accurate and consistent data.
Once the class has decided on the variables, I direct them to look at setup at one of the tables in the back of the room. I show them that it is the same setup that they made observations on during the Pre-Lab Discussion except there is a motion sensor attached. As in the picture below, the motion sensor is attached to the top of the elevated track. During this lab students release the cart from the top and it will roll down the ramp.
I like for my students to know how the equipment works. I tell them that the motion sensor collects the time and the position data at the same time. I explain that it works similar to how dolphins use echolocation and that the device uses sound waves to determine the distance of the cart to the sensor.
After I tell them about the setup, I tell them that there are roles for this lab activity. I do this to make sure all of the tasks are done and that everyone is doing something. The roles are (1) Cart Releaser, to release the cart at the top of the track, (2) Cart Catcher, to stop the cart before it hits the motion detector, (3) Plotly Grapher, to copy the data into Plotly from the DataStudio program, and (4) Lab Summary Creator, to make a copy and share the lab summary with all of the group members. After I explain the roles, I give them about 10 minutes to collect all of the data using the motion sensor and DataStudio, data collection software, and put it on Plotly. The data that is collected in DataStudio includes time, position and velocity at multiple points of the cart's journey. The program then provides students with two data tables: position & time and velocity & time. Students use those data points in Plotly to produce two graphs.
After students have collected the data, I tell each group as they finish that I want them to create a lab summary from their lab summary template that they use for each paradigm lab. I direct students to take a screenshot of their graphs that they have acquired through DataStudio (the program that we use to collect data from PASCO equipment) and put them into the lab summary. I have students complete the lab summary because it allows them to take a deeper look at the data they collected and what the graph is representing.
When all of the students have started their lab summaries, I tell them my expectations for this lab and how it is different from the labs we have done previously. There are two graphs that are created from their data: a position vs. time graph and a velocity vs. time graph. I tell my students that I would like to see 2 answers to each section or question in the summary, one for each graph. The most important parts for me to see are correct mathematical models and written relationships. When I am walking around assisting students I like to focus on those sections to make sure they are answering them correctly.
When students have finished with their lab summaries, I ask them to write the important concepts and information on a whiteboard for an upcoming discussion about the relationship between position, velocity acceleration and time. I tell them that each whiteboard should include a sketch of each graph and that each graph include the axis labels and units as well as a mathematical model.
When the students have completed their whiteboards, they circle up with their whiteboards for a discussion. The students have for the most part drawn a parabola for the position vs. time graph and a sloping line for the velocity vs. time graph. The reason that I have the students participate in this discussion is to help them to decipher what information is important from the lab and what the data are telling them.
At the beginning of the discussion, the focus is on their experimental procedure and their interpretations of the parabolic position vs. time graph. The first question that I ask them is "Do these position versus time graphs look different than last unit? If so, then how?" I hope that students can describe that the displacement during each time interval increases over the previous time interval and that since the object travels greater distances in each successive time interval, its velocity is increasing. I then ask students to look at the mathematical model from the position vs. time graphs and see what similarities and differences there are between each group's models. I try to focus students on the y and x variables to make sure that everyone agrees.
The second part of the discussion is where I like to focus on the velocity vs. time graph. I treat this part of the discussion similar to the position vs. time graph, asking students how these graphs look different the graphs from the previous unit, hoping they will see there is a changing velocity. I ask them to look at the mathematical models of each group and see any similarities or differences. Once the students agree on a mathematical model, I ask them to try to tell me what the slope and y-intercept represents. Through discussion, students recognize that slope is y over x, which is velocity over time, which is what we call acceleration. Similarly, the y-intercept represents the initial velocity.
Finally, I have students look at the slope values from each graph and ask them what they notice about the values. I help students to see that the slope on the position vs. time graph is half of the slope on the velocity vs. time graph. In other words, in our mathematical model of the position vs. time graph, the constant in front of x squared represents one-half of the acceleration. At the end, I ask students to recall what the slope represents on a velocity vs. time graph. When they say acceleration, I tell them that this is one of the major points we will be discussing the next few lessons.
After the whiteboard discussion, I ask students to watch the Uniform Acceleration Video and take notes for homework. I show them a preview of the video and say that there are a lot of pictures of graphs. I tell them to write down the pictures as they go through the notes and that we will expand on the notes next class. I have students watch this video to give them a exposure to the different representations of uniform accelerated motion. I provide my students with as many ways to learn this new material as possible. This video helps to prepare them for the next class where they will be predicting and then collecting data from 7 different stations or situations of an accelerating object.