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Homework Help: AP Calc Free Answer Problem:Change Over Time

  1. Jan 27, 2008 #1
    1. The problem statement, all variables and given/known data
    A Particle Moves along the x-axis so that its velocity v at time t [tex]\geq[/tex] 0 is given by v(t)=Sin(x[tex]^{2}[/tex]). The Graph of V is shown above for 0 [tex]\geq[/tex] t [tex]\geq[/tex] [tex]\sqrt{5\pi}[/tex]. The Position of the particle at time t is x(t) and its position at time t=0 is x(0)=5

    2. Relevant equations
    Find the total Distance traveled b the particle from time t=0 to t=3.

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data
    We just started on integration so i figured we would need find the displacement equation by integrating the velocity equation, which would be finding:
    [tex]\int[/tex] Sin(x[tex]^{2}[/tex] dt [0,3]. From here i have no idea how to do the equation since we're only 2 weeks into integration and have barely touched [tex]\mu[/tex] Substitution
    Last edited: Jan 27, 2008
  2. jcsd
  3. Jan 27, 2008 #2


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    Homework Helper

    The only way I can see to do it is to take the taylor series of sinx and replace all the x's by x^2 and then approximate the terms.
  4. Jan 27, 2008 #3
    oh thanks, in your opinion do you think that this problem is quite difficult for an AB AP Calculus Class?
  5. Jan 27, 2008 #4


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    Gold Member

    If the graph of the velocity is given, can you use this alone to find the distance? Remember the original definition of the integral of a function!

    [also remember that as in real life, not all information available to you need be relevant.]
    Last edited: Jan 27, 2008
  6. Jan 27, 2008 #5
    Oh. Are you referring to a of a Rieman's Sum approach to solving the equation by means of RRAM/MRAM/LRAM, Simpsons, Trapezoidal rule?
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