Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The kinematics of motion in one dimension Problem-solving strategies Motion Diagrams and Pictorial Diagrams Chapter 2 Motion in One Dimension 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

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-34 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:

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Pictorial Diagrams Slide 2-12

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-4 Pictorial Diagram Example 1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-4 Pictorial Diagram Example 2

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A.at t = 2 s. B.at t = 1 s and at t = 3 s. C.at t = 1 s, 2 s, and 3 s. D.P and Q never pass one another. Slide 2-34 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? Two Ships Passing in the Night

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A. B.at t = 1 s and at t = 3 s. C. D. Slide 2-34 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? Two Ships Passing in the Night

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A.P and Q have the same velocity at 2 s. B.P and Q have the same velocity at 1 s and 3 s. C.P and Q have the same velocity at 1 s, 2 s, and 3 s. D.P and Q never have the same velocity. Slide 2-34 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? Two Ships Passing in the Night

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A.P and Q have the same velocity at 2 s. Slide 2-35 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? Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Slide 2-15 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.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-16 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. Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-34 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.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-34 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?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-34 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

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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 Checking Understanding

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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 Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 2-34 Start your engine (velocity and acceleration) On the on ramp to Interstate 25 a car accelerates at 7 m/s 2 from 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.