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Calculus Problem - Maximum Velocity, Derivatives, etc.

  1. Nov 27, 2007 #1
    [SOLVED] Calculus Problem - Maximum Velocity, Derivatives, etc.

    1. The problem statement, all variables and given/known data
    A particle moves along a line so that at any time t its position given by x(t)=2[tex]\Pi[/tex]t + cos2[tex]\Pi[/tex]t.

    What is the maximum velocity?

    2. Relevant equations
    We found:
    v(t) = 2[tex]\Pi[/tex] - sin2t[tex]\Pi[/tex](2[tex]\Pi[/tex])
    a(t) = 2[tex]\Pi[/tex](-cos2t*[tex]\Pi[/tex])(2[tex]\Pi[/tex])
    all values of t when particle's at rest in [0,3]: t=1/4, 5/4, 9/4

    3. The attempt at a solution

    We tried setting the acceleration to zero and got t = 1/4, and plugged that in to the velocity and got v(t) = 0, which makes no sense because the max velocity is not when it is at rest.

    Any help would be GREATLY appreciated ... I have been working at this for 6 hours and am afraid that I am slowly withering away
    Last edited: Nov 27, 2007
  2. jcsd
  3. Nov 27, 2007 #2


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    Science Advisor

    a(t) is NOT zero for t=1/4. You made a mistake.

    If the cosine of something is zero, what is the sine? (This is the quick way to do this problem ...)
  4. Nov 27, 2007 #3
    How is a(1/4) not zero? You'd have:

    [tex] a(1/4) = -4 \pi^2 cos(2(1/4) \pi) [/tex]

    The cosine of pi over 2 is zero.

    The thing is that he's missing values for when a(t) is zero. t should have values of 1/4, 3/4, 5/4, 7/4, and 9/4. Some of these values, when plugged into the velocity equation, do not amount to zero velocity.
  5. Nov 27, 2007 #4
    thank you hotcommodity! i see that now! you are a lifesaver, truly.
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