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									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  at
              t
               vi  v f
  3. vavg 
                   2
                 1
  4. x  vi t  at 2
                 2
    v2  vi2  2ax
  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

								
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