The kinematics of motion in one dimension Problem-solving strategies

1. Chapter 2 Motion in One Dimension • The kinematics of motion in one dimension • Problem-solving strategies • Motion Diagrams and Pictorial Diagrams Topics: Sample question: Horses can run much much faster than humans, but if the length of the course is right, a human can beat a horse in a race. When, and why, can a man outrun a horse? Slide 2-1

2. Velocity and Acceleration Motion Graph Demos • For more practice with motion graphs and motion diagrams, use the Applet Tutorial Problems (Active Physics) in the Study Area in Mastering Physics. • The following problems are recommended: • 1.1 • 1.2 • 1.3 • 1.4 Slide 2-34

3. Pictorial Diagrams Slide 2-12

4. Pictorial Diagram Example 1 Slide 2-4

5. Pictorial Diagram Example 2 Slide 2-4

6. Two Ships Passing in the Night Ships P and Q move with the position graphs shown. Both ships are at the origin at t = 0s. When does one pass the other? at t = 2 s. at t = 1 s and at t = 3 s. at t = 1 s, 2 s, and 3 s. P and Q never pass one another. Slide 2-34

7. Two Ships Passing in the Night Ships P and Q move with the position graphs shown. Both ships are at the origin at t = 0s. When does one pass the other? at t = 1 s and at t = 3 s. Slide 2-34

8. Two Ships Passing in the Night Ships P and Q move with the position graphs shown. Both ships are at the origin at t = 0s. Do P and Q ever have the same velocity? If so, at what time or times? P and Q have the same velocity at 2 s. P and Q have the same velocity at 1 s and 3 s. P and Q have the same velocity at 1 s, 2 s, and 3 s. P and Q never have the same velocity. Slide 2-34

9. Answer Ships P and Q move with the position graphs shown. Both ships are at the origin at t = 0s. Do P and Q ever have the same velocity? If so, at what time or times? P and Q have the same velocity at 2 s. Slide 2-35

10. Checking Understanding A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? A. B. C. D. Slide 2-15

11. Answer A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? C. Slide 2-16

12. Where’s the train? A train is moving at a steady 30 m/s. At t = 0, the engine passes a signal light at x = 0. Without using any formulas, find the engine's position at t = 1s, 2s, and 3s. Express your reasoning in words. Slide 2-34

13. Velocity to Position: Example 1 Find the position at times t = 1, 2, 3, 4, and 5 seconds. Assume x (t = 0 sec) = 0 m. What is the displacement of the object between t = 1s and t = 3 s? Slide 2-34

14. Velocity to Position: Example 2 • Describe in words the motion of the object whose velocity graph is given below. What is happening at t = 2 s? • Draw a motion diagram of the objects motion. • Draw the corresponding position vs. time graph. Assume initial position is 5 m. • Give an example of an object that would move this way Slide 2-34

15. Checking Understanding An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Slide 2-28

16. Answer An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Slide 2-29

17. Start your engine (velocity and acceleration) On the on ramp to Interstate 25 a car accelerates at 7 m/s2from rest. What is the car's velocity at 1 second after it starts from rest? 2 seconds? 3 seconds? 4 seconds? Express your reasoning in words. Slide 2-34