Car on an Incline

Activity 2

Return to Investigation 1 if you have not completed it.

 

Investigation 2

 

Scenario 2

Carolyn tried using different power levels for her car to see how much it needed to be able to keep going up the hill.

 

Leave the initialSpeed set to 3. Working with a partner, use the power slider to change the power from 10 to 11.5. As you slowly increase the power using the arrow keys, one partner should be watching the list of height differences while the other watches the graph. Keep an eye out for anything different, unusual, or interesting. Try again, this time trading roles so both partners have watched the graph change and also watched the table of differences change.

 

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1.     Above a certain power level, the car will never start rolling backward, no matter how long the hill is. Find at least one power value for which you believe this is true, and  use the time slider to move the red point from 0 seconds to 5 seconds.

 

Describe the car's trip for this power value.

 

 

 

2.     Explain why you believe the car won't start rolling backward for that value. (In other words, why do you think it will not begin to roll back down for some time that you can't see on this graph?)

 

 

3.     Now use the power slider, the graph, the table, and the list of differences to find the lowest power value for which the car won't start rolling backward.

a.     Describe the graph's shape for that power value. How is the graph's shape different from graphs at higher and lower power values?

 

 

b.     What kind of pattern does the list of differences have for that lowest power value?

 

 

c.     Use the time slider to move the red point from 0 seconds to 5 seconds. Describe the car's trip at this power value. Consider the direction and speed of the car.

 

 

Scenario 3

If the power level could be set so precisely that the car's speed is constant—that is, the car's height would change by exactly the same amount each second—the graph is a line. For the speed to be constant, the car would have to move the same distance each half-second.

 

Set the power slider to 10.94 and notice the shape of the graph.

 

4.     Eric said the graph for this power value was a picture of the car as it moved up the hill—as the car moves to the right, it also moves up. Write a few sentences explaining why this is incorrect. (Hint: Think about what the graph shows for other power values.)

 

 

Extension

5.     When the speed is constant, the car maintains whatever speed it had when it first touched the hill. Change the initialSpeed slider, which changes this speed. What happens to the graph when the car travels at a higher speed? Why does this make sense?

 


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