Analyzing and Graphing Accelerated Motion Based on the Energy, Machines, and Motion lab Addresses state standards Sci 9-11 PS1A, 9-11 PS1B Math 7.2.E, A1.4.C

Goals Describe the motion of a fan cart using words, graphs, and “oil drop” diagrams. Translate between a verbal description, a graph, or an “oil drop” diagram of motion. Engage: Page Keeley Assessment Probe Explore: Describing constant motion Explain: Fan cart lab activity Elaborate: Name that motion (translating motion descriptions) Evaluate: Translating motion descriptions Debrief (Later in the day)

From Uncovering Student Ideas in Physical Science by Page Keeley and Rand Harrington, page 23-30

Take 1 minute to answer on your own. Compare answers with partners for about 1 minute. Come up with a group answer to the graphing question. Share your group’s answer with the class.

Given whatever tools you have or can find around you, determine the velocity of your car. Is the velocity constant? How do you know? Devise a method to test if the velocity is constant. Summarize your method and results in a short paragraph on the provided note card. We know the velocity is constant if equally sized displacements are travelled in equal time intervals. The smaller the duration measured, the more accurate our proclamation that the velocity is constant.

The car moves equal intervals in equal amounts of time. Car is not speeding up or slowing down (or changing direction). Graph is a straight line. See example. example How do we know the car is not speeding up or slowing down between data points?

Now you will get a car that speeds up. Please be careful of the propeller. It can pinch your finger. You will also get a tape timer, a device that puts a mark on a paper every 0.1 s or s. Attach about 2 meters of tape to the back of your cart. Make a data table with about 10 position and corresponding time values. Use Excel to make a position vs. time graph for your car. I have put an Excel worksheet template online. Office 2007: When you are done with your spreadsheet and graph, give the file a creative name and it to me at

Time (s)Position (cm) Velocity (cm/s) (compared to the zero point) (compared to the zero point) To make a position vs time graph, plot time along the x- axis and position along the y-axis. Determine the best fit curve using Excel (either linear or polynomial) to Excel templates: 2007: Sample data

The car moves increasing distances in equal amounts of time. Graph is a upward curve. How do we know the car is not constant or slowing down between data points? Compare different cars. Compare

What does each parameter represent here? Here y is position, x is time, is 1/2a, is initial velocity and is initial position.

The slope of a position vs. time graph is the velocity. If the velocity is changing, the slope at each point represents the velocity at that point. The slope of a velocity vs. time graph is the acceleration. Definition of acceleration: Acceleration = change in velocity/change in time a=∆v/ ∆t The more the velocity changes for a set time interval, the greater the acceleration. Acceleration can be positive or negative

Describe the motion of the object that made each of these tapes. Justify your answer.

Let’s practice this more.more Constant velocity High acceleration Low acceleration

(If time permits) Open the Name that Motion simulationsimulation Work in your groups. Just enter one name on the screen but fill out your own answer sheet. View each motion. Type the number of the description on the worksheet that matches the motion.worksheet

From Uncovering Student Ideas in Physical Science by Page Keeley and Rand Harrington, page Take one minute to answer on your own. Talk to your partners for about two minutes and compare answers. On the back of your sheet, write your group answer and explanation. Share your group’s answer with the class.

Bill has confused the position vs. time graph with a picture of the path of motion. He needs help understanding what a position vs. time graph tells him. Patti seems to understand that a steeper line means faster and less steep line means slower. But she does not adequately describe the meaning of the flat line. Kari has the best answer. She seems to understand that a flat line on a position vs. time graph means no change in position, an object that is not moving. Mort has confused the position vs. time graph with a picture of the path of motion. He needs help understanding what a position vs. time graph tells him.