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Math Help - Don't get this velocity question?

  1. #1
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    Don't get this velocity question?

    Particle moves along the x-axis so that its velocity at time t greater or equal to 0 is given by v(t) = sin(t^2)

    Graph shown for 0 to sqrt(5pi). Position of the particle @ time t is x(t) and its position at time t = 0 is x(0) = 5

    a) Find the acceleration of the particle at the time t = 3

    I got the answer as 0.. IS this right??

    The other ones I don't get,,,

    b) Find the total distance traveled by the particle from time t = 0 to t= 3..

    Do I take the integral of sin(t^2)??? from 0 to 3??

    c) FInd the postion of the particle at time t = 3

    d) for 0 to sqrt(5pi) with t in between.. find the time t at which the particle is farthest to the right. Explain your answer.
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  2. #2
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    Quote Originally Posted by elpermic View Post
    Particle moves along the x-axis so that its velocity at time t greater or equal to 0 is given by v(t) = sin(t^2)

    Graph shown for 0 to sqrt(5pi). Position of the particle @ time t is x(t) and its position at time t = 0 is x(0) = 5

    a) Find the acceleration of the particle at the time t = 3

    I got the answer as 0.. IS this right??

    The other ones I don't get,,,

    b) Find the total distance traveled by the particle from time t = 0 to t= 3..

    Do I take the integral of sin(t^2)??? from 0 to 3??

    c) FInd the postion of the particle at time t = 3

    d) for 0 to sqrt(5pi) with t in between.. find the time t at which the particle is farthest to the right. Explain your answer.
    first of all, note that this problem requires the use of a graphing calculator.

    a. a(3) = v'(3) = -5.467 ... use the nDeriv function on your calculator.

    b. total distance = \int_0^3 |v(t)| \, dt = 1.702 ... use the fnInt function on your calculator.

    c. x(3) = x(0) + \int_0^3 v(t) \, dt = 5.774 ... again, use fnInt

    d. looking at the graph, the particle will be farthest to the right at the first time v(t) = 0 , at t = 1.772
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