Motion in One DimensionSection 1 Preview Section 1 Displacement and VelocityDisplacement and Velocity Section 2 Extra QuestionsExtra Questions

Motion in One DimensionSection 1 What do you think? Is the book on your instructor’s desk in motion? –Explain your answer.

Motion in One DimensionSection 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.

Motion in One DimensionSection 1 Click below to watch the Visual Concept. Visual Concept Frame of Reference

Motion in One DimensionSection 1 Displacement (  x)  Straight line distance from the initial position to the final position (change in position) Can be positive or negative

Motion in One DimensionSection 1 Displacement What is the displacement for the objects shown? Answer: 9 cm Answer: -15 cm

Motion in One DimensionSection 1 Displacement - Sign Conventions Right (or east) ---> + Left (or west) ---> – Up (or north) ----> + Down (or south) ---> –

Motion in One DimensionSection 1 Average Velocity The units can be determined from the equation. –SI Units: m/s –Other Possible Units: mi/h, km/h, cm/year Average velocity is displacement divided by the time interval.

Motion in One DimensionSection 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 km to the east. If the first half of the distance is driven at 50.0 km/h and the second half at a km/h, what is the average velocity? –Answer: 66.7 km/h to the east

Motion in One DimensionSection 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.

Motion in One DimensionSection 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

Motion in One DimensionSection 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

Motion in One DimensionSection 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

Motion in One DimensionSection 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?

Motion in One DimensionSection 2 Graphing Velocity The slope (rise/run) of a velocity/time graph is the acceleration. –Rise is change in v –Run is change in t This graph shows a constant acceleration. Average speed is the midpoint.

Motion in One DimensionSection 2 Graph of v vs. t for a train Describe the motion at points A, B, and C. Answers –A: accelerating (increasing velocity/slope) to the right –B: constant velocity to the right –C: negative acceleration (decreasing velocity/slope) and still moving to the right

Motion in One DimensionSection 3 Graphing Free Fall Based on your present understanding of free fall, sketch a velocity-time graph for a ball that is tossed upward (assuming no air resistance). –Is it a straight line? –If so, what is the slope? Compare your predictions to the graph to the right.

Motion in One DimensionSection 3 Multiple Choice Use the graphs to answer questions 1–3. 1. Which graph represents an object moving with a constant positive velocity? A. IC. III B. II D. IV

Motion in One DimensionSection 3 Multiple Choice Use the graphs to answer questions 1–3. 1. Which graph represents an object moving with a constant positive velocity? A. IC. III B. II D. IV

Motion in One DimensionSection 3 Multiple Choice, continued Use the graphs to answer questions 1–3. 2. Which graph represents an object at rest? F. I H. III G. II J. IV

Motion in One DimensionSection 3 Multiple Choice, continued Use the graphs to answer questions 1–3. 2. Which graph represents an object at rest? F. I H. III G. II J. IV

Motion in One DimensionSection 3 Multiple Choice, continued Use the graphs to answer questions 1–3. 3. Which graph represents an object moving with a constant positive acceleration? A. IC. III B. II D. IV

Motion in One DimensionSection 3 Multiple Choice, continued Use the graphs to answer questions 1–3. 3. Which graph represents an object moving with a constant positive acceleration? A. IC. III B. II D. IV

Motion in One DimensionSection 3 Multiple Choice, continued 4.A bus travels from El Paso, Texas, to Chihuahua, Mexico, in 5.2 h with an average velocity of 73 km/h to the south.What is the bus’s displacement? F. 73 km to the south G. 370 km to the south H. 380 km to the south J. 14 km/h to the south

Motion in One DimensionSection 3 Multiple Choice, continued 4.A bus travels from El Paso, Texas, to Chihuahua, Mexico, in 5.2 h with an average velocity of 73 km/h to the south.What is the bus’s displacement? F. 73 km to the south G. 370 km to the south H. 380 km to the south J. 14 km/h to the south

Motion in One DimensionSection 3 Multiple Choice, continued 5. What is the squirrel’s displacement at time t = 3.0 s? A. –6.0 m B. –2.0 m C m D m Use the position-time graph of a squirrel running along a clothesline to answer questions 5–6.

Motion in One DimensionSection 3 Multiple Choice, continued 5.What is the squirrel’s displacement at time t = 3.0 s? A. –6.0 m B. –2.0 m C m D m Use the position-time graph of a squirrel running along a clothesline to answer questions 5–6.

Motion in One DimensionSection 3 Multiple Choice, continued Use the position-time graph of a squirrel running along a clothesline to answer questions 5–6. 6.What is the squirrel’s average velocity during the time interval between 0.0 s and 3.0 s? F. –2.0 m/s G. –0.67 m/s H. 0.0 m/s J m/s

Motion in One DimensionSection 3 Multiple Choice, continued 6.What is the squirrel’s average velocity during the time interval between 0.0 s and 3.0 s? F. –2.0 m/s G. –0.67 m/s H. 0.0 m/s J m/s Use the position-time graph of a squirrel running along a clothesline to answer questions 5–6.

Motion in One DimensionSection 3 Short Response 10. In one or two sentences, explain the difference between displacement and distance traveled.

Motion in One DimensionSection 3 Short Response 10. In one or two sentences, explain the difference between displacement and distance traveled. Answer: Displacement measures only the net change in position from starting point to end point. The distance traveled is the total length of the path followed from starting point to end point and may be greater than or equal to the displacement.

Motion in One DimensionSection 3 Short Response, continued 11. The graph shows the position of a runner at different times during a run. Use the graph to determine the runner’s displacement and average velocity: a. for the time interval from t = 0.0 min to t = 10.0 min b. for the time interval from t = 10.0 min to t = 20.0 min c. for the time interval from t = 20.0 min to t = 30.0 min d. for the entire run

Motion in One DimensionSection 3 Short Response, continued 11. The graph shows the position of a runner at different times during a run. Use the graph to determine the runner’s displacement and average velocity. Answers will vary but should be approximately as follows: a. for t = 0.0 min to t = 10.0 min Answer: m, +4.0 m/s b. for t = 10.0 min to t = 20.0 min Answer: m, +2.5 m/s c. for t = 20.0 min to t = 30.0 min Answer: +900 m, +2 m/s d. for the entire run Answer: m, +2.7 m/s