VIEWS: 32 PAGES: 31 POSTED ON: 3/23/2011
Motion in One Dimension Section 1 Preview Section 1 Acceleration Section 2 Extra Questions Motion in One Dimension Section 2 What do you think? • Which of the following cars is accelerating? – A car shortly after a stoplight turns green – A car approaching a red light – A car with the cruise control set at 80 km/h – A car turning a curve at a constant speed • Based on your answers, what is your definition of acceleration? Motion in One Dimension Section 2 Acceleration • Rate of change in velocity • What are the units? – SI Units: (m/s)/s or m/s2 – Other Units: (km/h)/s or (mi/h)/s • Acceleration = 0 implies a constant velocity (or rest) Motion in One Dimension Section 2 Classroom Practice Problem • Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s. – Answer: 9.3 m/s2 downward Motion in One Dimension Section 2 Direction of Acceleration Describe the motion of an object with vi and a as shown to the left. Vi a + + • Moving right as it speeds up + - • Moving right as it slows down - - • Moving left as it speeds up - + • Moving left as it slows down Motion in One Dimension Section 2 Acceleration Click below to watch the Visual Concept. Visual Concept Motion in One Dimension Section 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. vi v f vavg 2 Motion in One Dimension Section 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 Dimension Section 2 Useful Equations x 1. vavg t v 2. aavg v f vi at t vi v f 3. vavg 2 1 4. x vi t at 2 2 v2 vi2 2ax 5. f Motion in One Dimension Section 2 Classroom Practice Problems • A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval? – Answer: 84 m • An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing? – Answer: -18.0 m/s2 Motion in One Dimension Section 2 Now what do you think? • Which of the following cars is accelerating? – A car shortly after a stoplight turns green – A car approaching a red light – A car with the cruise control set at 80 km/h – A car turning a curve at a constant speed • Based on your answers, what is the definition of acceleration? • How is acceleration calculated? • What are the SI units for acceleration? Motion in One Dimension Section 3 What do you think? • Observe a metal ball being dropped from rest. – Describe the motion in words. – Sketch a velocity-time graph for this motion. • Observe the same ball being tossed vertically upward and returning to the starting point. – Describe the motion in words. – Sketch a velocity-time graph for this motion. Motion in One Dimension Section 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 Dimension Section 3 Velocity and Acceleration of an Object at its High Point Click below to watch the Visual Concept. Visual Concept Motion in One Dimension Section 3 Preview • Multiple Choice • Short Response • Extended Response Motion in One Dimension Section 3 Multiple Choice, continued Use the position-time graph of a squirrel running along a clothesline to answer questions 5–6. 5. What is the squirrel’s displacement at time t = 3.0 s? A. –6.0 m B. –2.0 m C. +0.8 m D. +2.0 m Motion in One Dimension Section 3 Multiple Choice, continued Use the position-time graph of a squirrel running along a clothesline to answer questions 5–6. 5. What is the squirrel’s displacement at time t = 3.0 s? A. –6.0 m B. –2.0 m C. +0.8 m D. +2.0 m Motion in One Dimension Section 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. +0.53 m/s Motion in One Dimension Section 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. +0.53 m/s Motion in One Dimension Section 3 Multiple Choice, continued 7. Which of the following statements is true of acceleration? A. Acceleration always has the same sign as displacement. B. Acceleration always has the same sign as velocity. C. The sign of acceleration depends on both the direction of motion and how the velocity is changing. D. Acceleration always has a positive sign. • Motion in One Dimension Section 3 Multiple Choice, continued 7. Which of the following statements is true of acceleration? A. Acceleration always has the same sign as displacement. B. Acceleration always has the same sign as velocity. C. The sign of acceleration depends on both the direction of motion and how the velocity is changing. D. Acceleration always has a positive sign. • Motion in One Dimension Section 3 Multiple Choice, continued 8. A ball initially at rest rolls down a hill and has an acceleration of 3.3 m/s2. If it accelerates for 7.5 s, how far will it move during this time? F. 12 m G. 93 m H. 120 m J. 190 m Motion in One Dimension Section 3 Multiple Choice, continued 8. A ball initially at rest rolls down a hill and has an acceleration of 3.3 m/s2. If it accelerates for 7.5 s, how far will it move during this time? F. 12 m G. 93 m H. 120 m J. 190 m Motion in One Dimension Section 3 Short Response, continued 12. For an object moving with constant negative acceleration, draw the following: a. a graph of position vs. time b. a graph of velocity vs. time For both graphs, assume the object starts with a positive velocity and a positive displacement from the origin. Motion in One Dimension Section 3 Short Response, continued 12. For an object moving with constant negative acceleration, draw the following: a. a graph of position vs. time b. a graph of velocity vs. time For both graphs, assume the object starts with a positive velocity and a positive displacement from the origin. Answers: Motion in One Dimension Section 3 Short Response, continued 13. A snowmobile travels in a straight line. The snowmobile’s initial velocity is +3.0 m/s. a. If the snowmobile accelerates at a rate of +0.50 m/s2 for 7.0 s, what is its final velocity? b. If the snowmobile accelerates at the rate of –0.60 m/s2 from its initial velocity of +3.0 m/s, how long will it take to reach a complete stop? Motion in One Dimension Section 3 Short Response, continued 13. A snowmobile travels in a straight line. The snowmobile’s initial velocity is +3.0 m/s. a. If the snowmobile accelerates at a rate of +0.50 m/s2 for 7.0 s, what is its final velocity? b. If the snowmobile accelerates at the rate of –0.60 m/s2 from its initial velocity of +3.0 m/s, how long will it take to reach a complete stop? Answers: a. +6.5 m/s b. 5.0 s Motion in One Dimension Section 3 Extended Response 14. A car moving eastward along a straight road increases its speed uniformly from 16 m/s to 32 m/s in 10.0 s. a. What is the car’s average acceleration? b. What is the car’s average velocity? c. How far did the car move while accelerating? Show all of your work for these calculations. Motion in One Dimension Section 3 Extended Response 14. A car moving eastward along a straight road increases its speed uniformly from 16 m/s to 32 m/s in 10.0 s. a. What is the car’s average acceleration? b. What is the car’s average velocity? c. How far did the car move while accelerating? Answers: a. 1.6 m/s2 eastward b. 24 m/s c. 240 m Motion in One Dimension Section 3 Extended Response, continued 15. A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m. a. How long does it take the ball to reach its highest point? b. How long is the ball in the air? Show all of your work for these calculations. Motion in One Dimension Section 3 Extended Response, continued 15. A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m. a. How long does it take the ball to reach its highest point? b. How long is the ball in the air? Show all of your work for these calculations. Answers: a. 2.55 s b. 5.18 s