To conduct the experiment, each person in your group should be given a role:

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1 Varying Motion NAME In this activity, your group of 3 will collect data based on one person s motion. From this data, you will create graphs comparing displacement, velocity, and acceleration to time. To understand the difference between displacement and distance, consider this example: A business person flew from Washington, DC to New York City. Taking off again, he traveled to Chicago. After a brief business meeting, he had a direct flight back to Washington, DC. The distance that he traveled was approximately 2,200 miles, but his displacement was 0 miles. Distance is a measured value with a unit, such as 5 miles. Displacement measures how far you have traveled from your starting point. It also has a direction, such as 5 miles North. It is not possible to have a negative distance, but it is possible to have a negative displacement. For example, if you define North as positive, moving 5 miles South gives you a displacement of 5. Similarly, there is a difference between speed and velocity. Velocity is the rate of change of your displacement, so it has a measured value, unit, and direction. Speed is the rate of change of distance, so like distance it has no direction and cannot be negative. Measuring Displacement To conduct the experiment, each person in your group should be given a role: Timer Walker Marker Uses the stop watch to time the walker for 60 seconds. The timer should call out the time every 4 seconds, so the marker can mark the intervals. Walks forward in one direction within your group s designated space. The walker should vary the rate they are walking at, alternating between slower and faster walking speeds. Make sure not to outrace the marker! Tracks the walker s displacement. Before beginning, mark the starting line with a piece of masking tape. Then, mark where the walker is when the timer calls out time every 4 seconds.

2 1. Run the experiment once, and then measure the displacement from the starting line to each of the tape markers as a group. Note: The displacement is the distance from the starting line to each tape marker, not the distance between tape markers. Record the displacements in the table on the next page TIME (sec) DISPLACEMENT (ft OR m) Create a displacement vs. time graph on a separate sheet of paper. Draw a smooth curve through the plotted points. Which is the dependent variable? Which is the independent variable? 3. What information is given by slope in a displacement vs. time graph? Why does the slope of the line change for different time intervals? 4. All of the displacements in this activity are positive. Why? What does this mean?

3 Measuring Instantaneous Velocity 5. Draw points on your displacement vs. time graph at the times indicated in the first column of the table below. For each point, draw a tangent line and find the slope of the line. Record the slopes in the table. TIME (sec) SLOPE (ft/sec OR m/sec) 6. Create a velocity vs. time graph on a separate sheet of paper. In your graph make velocity the dependent variable and time the independent variable. Draw a smooth curve through the plotted points. 7. What information is given by slope in a velocity vs. time graph? Why does the slope change for different time intervals? 8. Were any of the instantaneous velocities negative? What circumstance could create a negative velocity?

4 Measuring Instantaneous Acceleration 9. Draw points on your velocity vs. time graph at the times indicated in the first column of the table below. For each point, draw a tangent line and find the slope of the line. Record the slopes in the table. TIME (sec) SLOPE (ft/sec 2 OR m/ sec 2 ) Create an acceleration vs. time graph on a separate sheet of paper. In your graph make acceleration the dependent variable and time the independent variable. Draw a smooth curve through the plotted points. 11. What information is given by slope in a velocity vs. time graph? Why does the slope change for different time intervals? 12. Were any of the instantaneous accelerations negative? What circumstance could create a negative acceleration?

5 Measuring Area 13. Look back at your velocity vs. time graph. Draw points on the velocity vs. time graph at the times indicated in the first column of the table in Question 14. Describe a method you could use to estimate the area under the graph for intervals from 0 to each indicated time. Draw a picture if this helps your explanation. 14. Find the areas under the graph for intervals from 0 to each indicated end time. Then, record the displacement at each end time from your displacement vs. time graph. END TIME (sec) AREA UNDER THE VELOCITY VS. TIME GRAPH FOR THE INTERVAL FROM t = 0 TO END TIME DISPLACEMENT FROM DISPLACEMENT VS. TIME GRAPH 15. Compare the values in the second and third columns of the table. What do you notice? 16. What information is calculated from the area under the graph of a velocity vs. time graph? 17. What information do you think is calculated from the area under the graph of an acceleration vs. time graph?