Lesson 2-4: Average vs. Instantaneous Velocity (Revisiting the Tortoise and Hare) Period: Date:

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1 Name: Period: Date: For this assignment: Re-read the Tortoise vs. the Hare story (2-1) All the needed information is on this assignment or in the reading Every question requires you to go back to previous answers 1. Describing the motion of the Tortoise and the Hare using words. Tortoise Hare 2. Finding change in position (displacement): Look in the story to find the length of the race: Starting position (p i ) = Ending Position (p f ) = Change in position in meters ( p): 3. Finding the Time Interval: Tortoise: Starting Time (t i ): Ending Time (t f ): Total time ( t): Hare: Starting Time (t i ): Ending Time (t f ): Total time ( t): 4. Calculating the average velocity: over the entire 1 kilometer-long course for both the Tortoise and the Hare during the race. a) Tortoise: pi = pf = Δp = t i = t f = Δt = b) Hare: Average velocity = Δp/Δt Tortoise: pi = pf = Δp = t i = t f = Δt = Average velocity = Δp/Δt Hare:

2 5. Calculating how long the Hare napped: a. The hare runs 5 km/hour (0.083 km/min), how many minutes passed while the hare ran the first 500 meters (0.5km) of the course? [1 kilometer (km) = 1,000 meters (m)] Time Passed ( t) for first 500 meters= b. How many minutes passed while the hare ran the last 500 meters? Time Passed ( t) for second 500 meters = c. How many minutes passed while the hare was napping? Time Passed ( t) during nap = 6. Calculate the average velocity of the Hare for each part of the race. a. First half (0 to 500m) = b. Napping (at 500m)= c. Second half (500m to 1000m)= 7. How does the average velocity of the Hare during the time interval that it napped, compare with the instantaneous velocity of the Hare at one instant during the nap? 8. GENERALIZING: When is the average velocity of an object during an interval of time EQUAL to the instantaneous velocity for any instant during that interval of time? 9. Create a position (vertical-axis) vs. time (horizontal-axis) graph with one line depicting the actions of the Tortoise and one line depicting the actions of the Hare during the race. Use a full sheet of graph paper. Be sure to title the graph, label both axes (including units), show the intervals on each axis, and identify each racer in a legend.

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4 10. Create a motion map for the both the Tortoise and the Hare. Tortoise 0km 0.5km 1km Hare 0km 0.5km 1km 11. Using the data you have generated above, make a velocity vs time graph for the Tortoise and a separate velocity vs. time graph for the Hare. Compare your graphs with a classmate. 12. Analysis Questions a. What do you think of the following statement, We cannot measure speed. Do you agree or disagree and why? b. What is the instantaneous velocity of the Tortoise at any point during the race? c. Is the Tortoise s instantaneous velocity the same or different than the Tortoise s average velocity? Why/how/when is that possible? d. Is the Hare s Instantaneous velocity ever equal to the Hare s average velocity for the entire race? Why/how/when is that possible? e. Why would someone agree that the Hare won the race? Why would someone agree that the Tortoise won the race? Explain your reasoning. Include supporting pieces of evidence from the story. You must use the words instantaneous velocity and average velocity in your answer.

5 EXTENSION Problem: The following year, the Hare challenged the Tortoise to a rematch. Below are the Velocity vs Time graphs for the race. 1. Did the Hare take a nap during this race? 2. What was the total distance of the race? (Hint: How fast was the Tortoise going each minute? How many minutes did he run?) 3. How far did the Hare go in the first 10 seconds of the race? Last 10 seconds? Middle 80 seconds? 4. Who won the race?

6 Make a Position vs Time Graph for the Tortoise and Hare race.