Exploring rate of change in motion problems Block 4 Student Activity Sheet
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1 1. Sketch the graph of each elevator ride described. [EX3, page2] a. The elevator starts on floor 4 and rises at a rate of 1 floor per second. b. The elevator starts on floor -3 rises at a rate of 2 floors per second. c. The elevator starts on floor 11 and descends at a rate of 1 floor per second. d. The elevator starts on floor 12 and descends at a rate of 2 floors per second. Page 1 of 8
![2. Consider this elevator graph. [EX3, page 3] a. Why does the graph have a horizontal segment at the end? The horizontal segment represents when the elevator is no longer moving.](/docs-images/93/112092887/images/2-2.jpg "The elevator has become stationary at a particular floor, but time continues to pass. b. What is the meaning of the point (2, -1) on the graph?")
2 2. Consider this elevator graph. [EX3, page 3] a. Why does the graph have a horizontal segment at the end? The horizontal segment represents when the elevator is no longer moving. The elevator has become stationary at a particular floor, but time continues to pass. b. What is the meaning of the point (2, -1) on the graph? At 2 seconds, the elevator is 1 floor below ground level. 3. REINFORCE Sketch a graph of the position of the elevator (elapsed time, distance from ground in floor numbers) as the elevator rose from the ground level to the 10th floor at a rate of 2 floors per second. Page 2 of 8
3 4. Use the animation to explore and match the graph by changing the elevator settings. [EX3, page 4] a. Elevator: Start: 12 Rate: -1 b. Elevator: Start: 10 Rate: -1 c. Elevator: Start: 12 Rate: -2 d. Elevator: Start: 3 Rate: -1 Page 3 of 8
4 e. Elevator: Start: 4 Rate: 0 f. Elevator: Start: -3 Rate: 4 5. Now look back over your work on matching elevator graphs as you answer the following questions. [EX3, page 5] a. How did you decide what the starting floor was? The starting floor is indicated by the point where the graph touches the y-axis, at time 0. b. How did you decide what the rate was? Determine the rate by looking at how far the elevator travels in 1 second. Look at the number of floors traveled between 0 and 1 second or between any other two points on the graph that indicate a 1-second interval. Page 4 of 8
5 6. Now think about all the work you have done with elevator graphs. [EX3, page 5] a. What were the rates when the elevator graphs looked the steepest? The graphs were steepest when the rates were described by numbers with large absolute values, like -3, 3, -4, or 4. b. What were the rates when the elevator graphs looked the least steep? The graphs were less steep when the rates were described by numbers closer to 0 like -1 or 1. Five descriptions of graphs are provided here. Use these descriptions to fill in the blanks in the statements about elevator motion. [EX3, page 6] the graph falls and is steeper the graph rises and is steeper the graph is a horizontal line the graph rises and is less steep the graph falls and is less steep 7. When the elevator pauses on a floor, the graph is a horizontal line. 8. When the elevator rises rapidly, the graph rises and is steeper. 9. When the elevator descends rapidly, the graph falls and is steeper. 10. When the elevator rises slowly, the graph rises and is less steep. 11. When the elevator descends slowly, the graph falls and is less steep. Page 5 of 8
6 12. REINFORCE Sketch the graph of each elevator ride described. a. Elevator: Start at floor 3 at rate -2. b. Elevator: Start at floor 11 at rate -2. c. Elevator: Start at floor 12 at rate -1. d. Elevator: Start at floor 12 at rate -3. Page 6 of 8
7 13. REINFORCE Sketch the graph of each elevator ride described. a. Elevator: Start at floor 11 at rate -1. b. Elevator: Start at floor 1 at rate -1. c. Elevator: Start at floor 1 at rate -1. d. Elevator: Start at floor 1 at rate 1. Page 7 of 8
8 14. REINFORCE Here is the graph of one elevator ride, shown in (Elapsed time in seconds, Distance from ground in floor numbers). Interpret the graph by answering the following questions. a. Where did the elevator start? How do you know? At floor 12. That is the point where the graph touches the y-axis, when time is 0. b. What happened between 0 and 4 seconds? How do you know? The elevator descended from floor 12 to floor 4. The graph fell on that interval from y = 12 to y = 4. c. What happened between 4 and 6 seconds? How do you know? The elevator stayed on the 4th floor. Its distance from the ground did not change, as indicated by the horizontal line. d. What happened between 8 and 9 seconds? How do you know? The elevator rose from the 8th floor to the 10th floor. The graph rose on that interval from y = 8 to y = 10. Page 8 of 8
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