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  • When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. For this question, many students will say the book is at rest, while others may say that Earth is moving so the book is moving as well. Students will sometimes say the molecules are moving so the book is moving. The point of the question is to lead them to the concept of a frame of reference.
  • Tell students that generally, the frame of reference we use is Earth. This is why many students said that the book was not in motion (for the previous slide).
  • Students sometimes just subtract the smaller from the larger number instead of the initial position from the final position.
  • These same sign conventions will apply to velocity, acceleration, force, momentum and so on.
  • As equations are written, show students how units for each quantity can be deduced from the equation. Have students determine the SI units before moving forward in the slide. This technique limits the amount of memorization required. See if students can suggest additional possible units of average velocity.
  • For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow them some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful. Show students how to obtain both answers to the first problem. For the second problem, point out the error in simply averaging the two velocities. This is wrong because the car spends more time traveling at the slower speed.
  • When discussing the second bullet point, ask students to describe the difference between distance and displacement. Then, ask students to explain why the third bullet point is true. (Answer: In a round trip, the displacement is zero, thus the average velocity is also zero. The speed is not zero because the distance traveled is not zero.)
  • Remind students that slopes have units. Many might just say that the slope is “1” instead of “1 m/s.”
  • Have students write their answers in their notes. Discuss the answer to object 1 before they answer questions 2 and 3. Many students will forget that velocity includes direction so they might simply answer “constant velocity” or “constant forward velocity”. This offers a chance to review the sign conventions for displacement and velocity.
  • Be sure students understand that the procedure of taking the tangent to find the velocity is only necessary when the velocity is not constant. Ask them how to draw a tangent line before showing the graph. Hold a meter stick up against the graph to show them the correct (and incorrect) way to draw a tangent line. Point out to the students that the tangent line has the same slope as the curve at that point. While the slope of the curve keeps changing, the slope of the line does not, so you can pick two points on the line and get the slope for the line (and for the curve at that point).
  • Students should now realize that the answer to the first question depends on the frame of reference chosen; there is no absolute motion. Some common terms used to describe motion include distance, displacement, average velocity, average speed, and instantaneous velocity.

Transcript

  • 1. Motion in One Dimension Section 1 Preview Section 1 Displacement and Velocity Section 2 Acceleration Section 3 Falling Objects © Houghton Mifflin Harcourt Publishing Company
  • 2. Motion in One Dimension Section 1 What do you think? • Is the book on Mr. Thompson’s desk in motion? – Explain your answer. © Houghton Mifflin Harcourt Publishing Company
  • 3. Motion in One Dimension Section 1 Frame of Reference • Motion – a change in position • Frame of reference – A point against which position is measured • Example: A train traveling between stations – It is in motion when measured against the track. – It is stationary when measured against a seat. © Houghton Mifflin Harcourt Publishing Company
  • 4. Motion in One Dimension Section 1 Displacement (∆ x ) • Straight line distance from the initial position to the final position (change in position) • Can be positive or negative © Houghton Mifflin Harcourt Publishing Company
  • 5. Motion in One Dimension Section 1 Displacement • What is the displacement for the objects shown? • Answer: 9 cm • Answer: -15 cm © Houghton Mifflin Harcourt Publishing Company
  • 6. Motion in One Dimension Section 1 Displacement - Sign Conventions • Right (or east) ---> + • Left (or west) ---> – • Up (or north) ----> + • Down (or south) ---> – © Houghton Mifflin Harcourt Publishing Company
  • 7. Motion in One Dimension Section 1 Average Velocity • Average velocity is displacement divided by the time interval. • The units can be determined from the equation. – SI Units: m/s – Other Possible Units: mi/h, km/h, cm/year © Houghton Mifflin Harcourt Publishing Company
  • 8. Motion in One Dimension Section 1 Classroom Practice Problems • A car travels 36 km to the north in 30.0 min. Find the average velocity in km/min and in km/h. – Answer: 1.2 km/min to the north or 72 km/h to the north • A car travels 100.0 km to the east. If the first half of the distance is driven at 50.0 km/h and the second half at a 100.0 km/h, what is the average velocity? – Answer: 66.7 km/h to the east © Houghton Mifflin Harcourt Publishing Company
  • 9. Motion in One Dimension Section 1 Speed • Speed does not include direction while velocity does. • Speed uses distance rather than displacement. • In a round trip, the average velocity is zero but the average speed is not zero. © Houghton Mifflin Harcourt Publishing Company
  • 10. Motion in One Dimension Section 1 Graphing Motion • How would you describe the motion shown by this graph? – Answer: Constant speed (straight line) • What is the slope of this line? – Answer: 1 m/s • What is the average velocity? – Answer: 1 m/s © Houghton Mifflin Harcourt Publishing Company
  • 11. Motion in One Dimension Section 1 Graphing Motion • Describe the motion of each object. • Answers – Object 1: constant velocity to the right or upward – Object 2: constant velocity of zero (at rest) – Object 3: constant velocity to the left or downward © Houghton Mifflin Harcourt Publishing Company
  • 12. Motion in One Dimension Section 1 Instantaneous Velocity • Velocity at a single instant of time – Speedometers in cars measure instantaneous speed. • Determined by finding the slope at a single point (the slope of the tangent) • What is the slope of the tangent line at t = 3.0 s? – Answer: approximately 12 m/s • What is the instantaneous velocity at t = 3.0 s? – Answer: approximately 12 m/s © Houghton Mifflin Harcourt Publishing Company
  • 13. Motion in One Dimension Section 1 Now what do you think? • Is the book on your instructor’s desk in motion? – How does your answer depend on the frame of reference? • What are some common terms used to describe the motion of objects? © Houghton Mifflin Harcourt Publishing Company