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Homework Help: Times when particle is moving in the positive x direction

  1. Nov 23, 2011 #1
    1. The problem statement, all variables and given/known data
    A particle has displacement x(t) = (t^3 - t^2)e^-t for times 0=<t=<9.
    Find its velocity v(t) and determine for what times the particle is moving
    in the positive x direction.

    2. Relevant equations
    Differentiating x(t) you get v(t)=-t(t^2-4t+2)e^-t

    3. The attempt at a solution
    I differentiated the equation but I am lost on how to get the times it is moving in the positive x direction.
  2. jcsd
  3. Nov 23, 2011 #2


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    Gold Member

    You have to determine where the derivative is positive. You do that by analyzing the signs of the factors of the derivative. You may need the quadratic formula to see where that quadratic expression changes sign.
  4. Nov 23, 2011 #3
    The answer is 2-sqrt2 < t < 2+sqrt2 but I'm still at a lose on how to get this. =/
  5. Nov 23, 2011 #4


    Staff: Mentor

    LCKurtz has given you a starting point.
  6. Nov 23, 2011 #5

    Ray Vickson

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    When in doubt, plot a graph (leaving out the exp(-t) factor, which does not change the sign of v(t)). In other words, plot f(t) = -t*(t^2 - 4t + 2) over a range of t values. The plot can be rough; all you really want to know is where f(t) changes sign.

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