AP Physics Lesson 1.a Kinematics Graphical Analysis Outcomes Interpret graphical evidence of motion (uniform speed & uniform acceleration). Apply an understanding of position time graphs to novel examples. Use graphical patterns of uniform velocity and uniform acceleration to derive kinematic equations. Solve graphical analysis problems and problems involving kinematic equations. Name Date Period Engage Examine the picture on the left. 1. What s happening? What is this picture about? 2. Are the children in danger? Why? Why not? Suppose you were driving a car and wanted to stop before reaching the children. (you know you should right?) The children are 20 meters away. 3. Which of the graphs below would best describe the motion of your car? a) b) c) d) 4. Explain why the other graphs won t work. 4b. Consider the list below and try to group events whose motion can be considered the same. How would you describe the motion of the events in the same group? You are not limited to a specific number of groups you will generate. Write the rationale for the groups you have chosen. Discuss your decision with the other students in your section and come to a consensus that you will share with the class. We will only discuss ideas here and we are not looking for a right answer. This will be your working hypothesis. 1. 2. 3. 4. 5. 6. 7. 8. 9. A marble rolling on a flat table A box sliding on a flat table A ball being dropped A cart rolling down a ramp A box sliding down a ramp A ball tossed straight up A ball tossed at an angle above the horizontal A toy gun shooting a dart horizontally A toy gun shooting a dart at an angle downward 1
Explore At your lab station you find a motion detector and a computer. Your teacher will demonstrate to you how to use the software program and the equipment. Indicate in the velocity graph where the velocity is zero. Draw your own line for zero velocity that is not the x-axis. You might need this in cases when the velocity is negative. It is very difficult to create these motions by walking in a way that the motion sensors will pick it up and display a clear graph. Instead you will be using the metal track and a ball or a motion cart. Think about ways to create set-ups where the ball or cart will display the motion of interest and will do it more smoothly and easier to record. Show your predictions to the teacher before using the motion detector. Type of motion (What do I think I will see on the graph?) (What did we actually observe?) Standing still in front of the detector. 2
Walking away from the detector at a uniform speed. Walking away from the detector while speeding up. 3
Type of motion (What do I think I will see on the graph?) (What did we actually observe?) Walking away from the detector while slowing down. 4
Type of motion (What do I think I will see on the graph?) (What did we actually observe?) Walking towards the detector at a uniform speed. Walking towards the detector while speeding up. 5
Type of motion (What do I think I will see on the graph?) (What did we actually observe?) Walking towards the detector while slowing down. Explain I Discuss your answers with your group. Conduct experiments to clear up disagreements. We use the term uniform to indicate that the quantity being described is not changing and remains the same. You can describe the shape of a line by indicating if the line is straight or curved, if it points up or down, if it is steeper at the beginning or the end when the line is curved. 5. What is the shape of a distance vs. time graph for an object that is not moving? 6. What is the shape of a velocity vs. time graph for an object that is not moving? 7. What is the shape of a distance vs. time graph for an object that is moving with a uniform speed? 8. What is the shape of a velocity vs. time graph for an object that is moving with a uniform speed? 9. What is the shape of a distance vs. time graph for an object that is moving with uniform acceleration? 10. What is the shape of a velocity vs. time graph for an object that is moving with uniform acceleration? 11. What is the shape of a distance vs. time graph for an object that is moving away from the motion detector? 12. What is the shape of a distance vs. time graph for an object that is moving towards the motion detector? 13. What is the shape of a velocity vs. time graph for an object that is moving away from the motion detector? 14. What is the shape of a velocity vs. time graph for an object that is moving towards the motion detector? 6
Use these graphs for 15-19. a) b) c) d) e) 15. Which graph represents an object moving with uniform positive acceleration? 16. Which graph(s) represents an object moving with uniform velocity? 17. Which graph represents a stationary object? 18. Which graph represents an object with uniform negative acceleration? 19. Which graph represents an object with the greatest uniform velocity? Use these graphs for 20-23. a) b) c) d) 20. Which graph represents an object moving with a uniform velocity? 21. Which graph represents an object moving with a uniform positive acceleration? 22. Which graph represents a stationary object? 23. Which graph represents an object with a uniform negative acceleration. 7
Elaborate I Now we will compare graphs for objects moving at different rates. The teacher will check your predictions before you can use the motion detector. Set Up (What do I think I will see on the graph?) (What did we actually observe?) 8
ball released from shallow ramp 9
Set Up (What do I think I will see on the graph?) (What did we actually observe?) ball released from steep ramp Explain II Discuss your answers with your group. Conduct experiments to clear up disagreements. 24. Compare the steepness of the lines for objects moving with different uniform speeds. Make a general statement 25. Compare the steepness of the curves for objects accelerating at different rates. 26. What general statement can you make about the meaning of the steepness of a motion graph? 10
Elaborate II Now we will test our skills at interpreting graphs. Describe how you think you will have to move in order to produce the example graphs. The teacher will check your predictions. Then check your predictions by actually walking back and forth in front of the detector to produce the given patterns. Describe how you actually moved to produce the same shape. The teacher will check your predictions before you can use the motion detector. Given graph (How do I think I will have to move to produce this shape?) (How did I actually have to move to produce this shape? Make one up to test your lab group partners! 11
27. Explain III 12
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Elaborate III 29. For the following motions predict and then check the corresponding kinematic graphs. Set Up (What do I think I will see on the graph?) (What did we actually observe?) Box sliding to a stop on a flat surface with friction 14
Cart rolling up an incline and rolling back down Ball tossed straight up into the air and falling back down 15