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Math Help - Acceleration/ total distance

  1. #1
    Member CalcGeek31's Avatar
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    Acceleration/ total distance

    Hi I was starting a total distance problem and got stuck.

    The acceleration of an object is given by a(t) =6sin(t) with initial velocity of -9.5. Find the total distance the object travels on the interval [0, pi] to the nearest integer.


    I know to take the integral and solve for velocity. I got the equation v(t) = -6cos(t) - 3.5. Firstly, is that right? and secondly How do I continue from there?
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  2. #2
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    velocity function is correct

    total distance traveled = \int_0^{\pi} |v(t)| \, dt
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  3. #3
    Member CalcGeek31's Avatar
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    Then am I right in saying that 11 would be the correct answer?
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  4. #4
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    no ... not the distance traveled.

    the displacement is -11, but in this case, displacement \neq distance traveled
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  5. #5
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    Oh so I would have to determine where the object changes direction and add the area from both curves?
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  6. #6
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    total distance = -\int_0^a v(t) \, dt + \int_a^{\pi} v(t) \, dt

    where a = \arccos\left(-\frac{7}{12}\right)
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  7. #7
    Member CalcGeek31's Avatar
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    Okay thank you so much, I have been having problems with that one for a while.
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