What is the Meaning of Velocity?
Kinematics Cycle 2 page 2
1. ENGAGE: Comparing Flights
Kinematics Cycle 2 page 2
1. ENGAGE: Comparing Flights
Materials: For each participant: index cards
Kinematics Cycle 2 page 2
2. EXPLORE: How Fast is Your Car
Compare the pictures above.
Plane A is traveling from Hays to Kansas City nonstop at 105 mph.
Plane B is traveling from Hays to Kansas City with an intermediate stop in Salina at 105 mph.
Plane C is traveling from Kansas City to
Hays nonstop at 105 mph.
- While in flight, which planes are traveling at the same speed?
- For the trip, which planes are traveling at the same average speed?
- For the trip, which planes are traveling with the same velocity?
- What do we need to know in order to determine speed?
- What do we need to know in order to determine velocity?
- Picture a toy electric car and design a question that could be used to test its speed.
- Write a testable question that could be explored by another team.
Starters for Testable Questions:
What happens if we______?
How is it possible to ______?
How can we______?
When comparing ______with
______which will______?
How (big/high/heavy/fast) can ______?
If we have ______, how ______?
Kinematics Cycle 2 page 2
2. EXPLORE: How Fast is Your Car?
Materials: electric toy car that travels at a constant speed, stopwatch, meter sticks, whiteboards
Kinematics Cycle 2 page 4
2. EXPLORE: How Fast is Your Car?
1. Write the testable question about determining the speed of your car your team chose to explore.
2. Given the materials supplied, design an investigation to answer the question you chose. Describe or illustrate your exploration.
3. Record observations and results (data) of your exploration.
4. Compare your results with the members of other groups. Whose car went the fastest? Is it easy to compare? Why or why not?
5. With your group, make a list of “Ideas about Kinematics”. Periodically, the class will visit these ideas.
6. With your group, make a list of “Questions about Kinematics” that you would like to have answered during our study.
Kinematics Cycle 2 page 4
3. EXPLAIN: What is Speed?
Materials: toy electric car that travels at a constant speed, stopwatch, meter stick
Kinematics Cycle 2 page 4
3. EXPLAIN: What is Speed?
- Express the speed of your toy electric car in meters/second (if you did that previously, write below your result).
- Compare your results with the members of other groups. Is it easier to compare than it was in the Explore activity? Why or why not?
- Think about what would be a reasonable speed, expressed in Système Internationale (SI) units (meters/second) for:
· a person taking a brisk walk:
· an ant crawling along a meter stick:
· a car on the interstate:
· the Concorde:
Kinematics Cycle 2 page 4
4. EXPLAIN: Is the Speed Constant?
Materials: For each group: pullback-type toy car that speeds up and slows down as it travels, stopwatch, meter sticks, masking tape, markers
Kinematics Cycle 2 page 4
4. EXPLAIN: Is the Speed Constant?
1. Determine the speed of the pullback toy car.
2. What did the speed of the car do as it traveled along? What speed did you calculate?
3. Consider the two halves of the trip (before the car reached the maximum speed and after that). How could you determine if the car was going faster during the first or during the second half of the trip?
4. Now consider only the first half of the trip - until car reaches its maximum speed. Further divide this section into two halves and compare speed of the car in each of them. Are they the same?
5. How could you find out details about the speed in any section of the trip? Come to a consensus in your group and be prepared to share your ideas with other groups.
6. Consider the children’s story, “The Tortoise and the Hare”. Which animal had the greatest speed? Be prepared to defend your answer.
7. What speed is measured by your vehicle’s speedometer – instantaneous or average? Explain your answer.
Kinematics Cycle 2 page 4
5 EXPLAIN: Mystery Walks II
Materials: None
Kinematics Cycle 2 page 4
7. EXPLAIN: Velocity Isn’t Speed
- Create a speed-time graph of the two Mystery Walks below:
2. He waited for 4 seconds before starting to walk slowly. He walked for a few seconds and then stopped.
3. She walked slowly for 3 seconds. Then she stood still for 4 seconds. Suddenly, during the last 3 seconds, she continued quite fast.
- What strategies did you use to help you match the correct graph to the story?
Kinematics Cycle 2 page 4
6. EXPLAIN: Graphing Speed
Materials: 6 stopwatches, meter stick, graph paper, masking tape, markers
Optional: graphing calculators, video camera for later playback
Kinematics Cycle 2 page 4
6. EXPLAIN: Graphing Speed
- Set up a straight 30-meter course. Every 5 meters, station a person with a stopwatch. Select a member of your group to be the runner who will travel the course in the manner described by the workshop leader. Have a person serve as a starter by standing near the beginning with his or her hand up. The lowering of the starter’s hand is the signal for the runner to begin and for all of the timers to start their watches. As the runner passes each timer, that timer should stop his or her watch. One person should serve as a recorder and collect all of the data and make a table of position and time.
- Create a graph of your data with distance in the vertical axis and time on the horizontal using the scale described by the workshop leader. Discuss with your group how this graph describes the motion of your runner and be prepared to share it with the whole group.
- How does the speed of the person affect the slope of the line?
- How could you determine average speed for the each trip?
- How could you determine instantaneous speed at any time for any of the walkers?
- Sketch on the next page the graph which shows how the instantaneous speed was changing for each of the runners (use different colors) at different segments of the 30m path. Prepare to share your results.
Kinematics Cycle 2 page 4
6. EXPLAIN: Graphing Speed
Kinematics Cycle 2 page 4
6. EXPLAIN: Graphing Speed
Kinematics Cycle 2 page 4
7. EXPLAIN: What Does the Graph Represent?
Cont.
Kinematics Cycle 2 page 16
7. EXPLAIN: What Does the Graph Represent?
Cont.
Kinematics Cycle 2 page 16
7. EXPLAIN: What Does the Graph Represent?
Cont.
1. Often we are asked to sketch a graph from words or descriptions, or we are asked to interpret information from a graph.
Choose the best graph to fit each of the situations described below.
a. I really enjoy cold tea or hot tea, but I loathe lukewarm tea.
b. Prices are now rising more slowly than at any time during the last five years.
c. The smaller the crates, the more crates we can load into the van.
d. After the concert there was a stunned silence. Then one person started clapping. Gradually, those around joined in, and soon everyone was clapping and cheering.
e. If the price of a ticket for a movie is too low, then the owners will lose money. If the price is too high, then too few people will attend and the owners still lose money. Therefore the movie theatre must choose a moderate price to charge for the tickets in order to stay profitable.
Kinematics Cycle 2 page 16
7. EXPLAIN: What Does the Graph Represent?
Cont.
Kinematics Cycle 2 page 16
7. EXPLAIN: What Does the Graph Represent?
Cont.
2. Make up three stories of your own to fit three of the remaining graphs.
3. What are the advantages/disadvantages to looking at a graph without a given scale?
4. If a group chose graph 11 for their answer to situation 1a, how could you justify their choice?
5. Draw your own graph for the following situation.
In the spring, the weeds around my house grew very quickly, and they needed mowed every week. But since we have had this hot dry spell, I have mowed less frequently.
Kinematics Cycle 2 page 16
8. EXPLAIN: Velocity Isn’t Speed
Materials: For each group: stopwatch, meter sticks, masking tape, markers
Kinematics Cycle 2 page 16
7. EXPLAIN: Velocity Isn’t Speed
1. Measure a flat (horizontal) distance of two or three meters that you can walk. Mark the ends of the line segment, calling one end A and the other end B.
2. Time someone walking at a constant speed from A to B. Calculate the average speed for the walk. Show your calculations below:
Distance: ______
Time: ______
Avg. Speed: ______
3. Have the same person walk back from B to A. Try for the same speed. Calculate the average speed for the walk. Show your calculations below:
Distance: ______
Time: ______
Avg. Speed: ______
4. When you walk from A to B you might have the same speed as when you walk from B to A, but you are doing something quite different. When the direction of travel is different, the result is different. When we talk about how fast something moves, we sometimes need to consider the direction of travel. When the direction doesn’t matter we use the term speed. When the direction does matter, we use the term velocity.
What were the velocities for the two walks above?
Average velocity walking from A to B: ______
Average velocity walking from B to A: ______
5. When you are driving a car on a one-way street, is your speed as important as your velocity? Why?
6. When driving on the freeway with the cruise control set, does your velocity stay constant along with your speed? Explain.
7. Based on your knowledge of the difference between the average speed and instantaneous speed, as well as the difference between the speed and the velocity - define the difference between average velocity and instantaneous velocity.
Kinematics Cycle 2 page 16
9. EXPLAIN: Mystery Walks III
Materials: For each group: position/time graph and a step size/time graph, a portion of the original Mystery Walk list from the workshop leader
Kinematics Cycle 2 page 16
9. EXPLAIN: Mystery Walks III
- Create velocity vs. time graph of one of the Mystery Walk (on the next page) that instructor assigns to your group. Prepare to explain to others what you did and why. Explain what strategies did you use to help you match the correct graph to the story?
- After all graphs have been presented, answer questions below:
- Did you learn from other groups any additional useful strategies for creating motion graphs? Write them down for your reference.
- What are the advantages/disadvantages to the two different types of graphs typically used for describing the motion (distance vs. time graph and velocity vs. time graph)?
- Could you reconstruct the motion story if you were given its graphical representation? Try the one below.
Kinematics Cycle 2 page 16
9. EXPLAIN: Mystery Walks III
Kinematics Cycle 2 page 16
9. EXPLAIN: Mystery Walks III
Kinematics Cycle 2 page 16
9. EXPLAIN: Mystery Walks III Cont.
Kinematics Cycle 2 page 16
9. EXPLAIN: Mystery Walks III Cont.
- She ran fast for 3 seconds, then slowly for 4 seconds. Then she went back to the beginning in 5 seconds.
- He walked backward very slowly. After 5 seconds he ran forward for 5 more seconds.
- She left home running really fast with step size of 1.5 meters. She walked for 3 seconds, but then she realized that she had forgotten her book. She stopped for a couple of seconds to decide what to do. Then she decided that it would be too late anyway, so she went back home slowly.
- From his house to the corner store is 10 meters. He ran to the store, spent 1 second looking at the CLOSED sign, and walked slowly back to his house.
- She decided to cross the park walking slowly at first but going faster and faster each step. It took her 5 seconds to get to the other side.
- He was going home, not in a rush. As he stepped into the street, he realized that a car was coming. He waited for the car, and then ran across the street. As soon as he got to the other side of the street, he walked slowly again.
- At first the old man walked very slowly, as if he was tired. Suddenly, when he was next to us, he started to run amazingly fast. After a few seconds he stopped and walked back to say, “I surprised you, didn’t I?”
- He waited for 4 seconds before starting to run with a step size of 1.5. He ran for a few seconds and then stopped.
- The dog ran off to catch the stick that his owner had thrown. As the dog grabbed the stick, he saw a rabbit. The dog held very still for a moment. Then, instead of running back to his owner, he crept very slowly toward the rabbit. When the dog was close to the rabbit, he jumped forward at great speed.
- First she went fast, at a steady pace. Then, at around 5 meters, she started to slow down. She went slower and slower until she stopped. She stood still for 4 seconds. Finally she walked slowly and steadily for a while.
- Trying not to wake anyone up, she walked very slowly with small steps. Once she got to the door, she began to run faster and faster. After 3 seconds of running, she stopped and sat down.
- Imagine someone walking back and forth two times between the chalkboard and her desk. She always walks fast toward the board and slowly towards the desk. At the end she remains still for 3 seconds.
- It is 8 meters between her bedroom and the kitchen. She walked into the kitchen slowly because she was half-asleep and then just stared at the room for a moment. Then she went back to bed very quickly.
Kinematics Cycle 2 page 16