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Homework Help: Kinematics of particles

  1. Jan 1, 2006 #1
    the motion of a particle is defined by x=2(t^3) - 18(t^2) + 48t - 16 where x=meter and t=sec.determine the total distance traveled when the acceleration is zero.

    the answer is 44m.

    pls help.....thanx......
     
  2. jcsd
  3. Jan 1, 2006 #2

    arildno

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    Hint:
    At what instant (t-value) is the acceleration 0?
     
  4. Jan 1, 2006 #3
    the value t=3 when the acc is zero
     
  5. Jan 1, 2006 #4

    arildno

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    And how may you use that info to answer the original question?
     
  6. Jan 1, 2006 #5
    oh,i found out d.it is the sum of t=0 to 3 rite??
     
  7. Jan 1, 2006 #6

    arildno

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    What do you mean by "sum"?
     
  8. Jan 1, 2006 #7
    the summation
     
  9. Jan 1, 2006 #8

    Doc Al

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    Another hint: At what time does the particle change direction?
     
  10. Jan 1, 2006 #9
    sorry,i not sure.....
     
  11. Jan 1, 2006 #10

    Doc Al

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    At the moment the particle changes direction, what is its speed?
     
  12. Jan 1, 2006 #11
    the velocity is zero
     
  13. Jan 1, 2006 #12

    arildno

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    Thus, within the interval t=0 to t=3, is there any instant at which the velocity is zero?
     
  14. Jan 1, 2006 #13

    Doc Al

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    Right. So find when the particle's velocity is zero.
     
  15. Jan 1, 2006 #14
    the particle's velocity = zero when t=4s and 2s
     
  16. Jan 1, 2006 #15

    Doc Al

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    Right. So to find the distance traveled by the particle from t = 0 to t = 3 seconds find the distance traveled from t = 0 to t = 2 and from t = 2 to t = 3 and add them.
     
  17. Jan 1, 2006 #16
    ya,i found it....thanx......
     
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