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Vector description of motion

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    What are the average velocity and average acceleration of the tip of the 2.4-cm-long hour hand of a clock in the interval from 12p.m. to 6p.m.

    I'm given the displacement which is 4.8 cm.
    I know the motion takes six hours
    I set my x axis at three-o-clock and my y-axis at 12


    2. Relevant equations

    Average velocity = displacement / change in time
    Average acceleration = change in velocity / change in time

    I
    3. The attempt at a solution

    The answer I get for velocity agrees with the back of the book:

    Avg Velocity = -0.8 j cm/hr

    But I have no clue how they get an average acceleration of -0.42 i cm/hr2.
    I don't understand why there would be an average acceleration if the hand moves at a constant speed. I understand that a change in direction changes acceleration, but I'm missing something.
     
  2. jcsd
  3. Oct 27, 2014 #2

    NascentOxygen

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    Staff: Mentor

    Hi ianperez. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    Acceleration = (change in velocity of a point on the tip) / elapsed time

    So you first need to determine magnitude and direction of the tip's velocity at the two times given.

    If the tip experienced no acceleration, it would not follow a curved path.
     
    Last edited by a moderator: May 7, 2017
  4. Oct 28, 2014 #3
    I got it! Thank you!!!

    The circumference is 4.8π so the velocity is 4.8π/12hrs=1.26cm/he
    Vi= 1.26i + 0j
    Vf = -1.26i + 0j
    Acceleration = (change in velocity of a point on the tip) / elapsed time
    A= -1.26-1.26 / 6hrs = -0.42cm/hr
     
  5. Oct 28, 2014 #4

    NascentOxygen

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    Staff: Mentor

    looks good
     
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