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Math Help - Integral question w/ velocity and acceleration

  1. #1
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    Integral question w/ velocity and acceleration

    a). The acceleration of a function a(t) (in m/s^2) and the initial velocity v(0) are given for a particle moving along a line.

    a(t) = 2t + 5. 0 < t<3
    v(0) = -6

    Find the velocity v(t) at time (t).

    b) The acceleration function a(t) (n m/s^2) and the initial velocity v(0) are given for a particle moving along a line.

    a(t) = 2t + 5. 0 < t<3
    v(0) = -6

    *note: It's less than or equal to, not just less than

    Find the total distance d traveled during the time interval.

    My question is once you integrate the expression, do you just solve what t is? Or is there more to it?
    Last edited by Jgirl689; February 8th 2010 at 07:14 PM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The distance traveled over a time period is the integral of the speed

    which is |v(t)|

    the velocity v(t) is the integral of the acceleration.

    Let's do it

    a(t) = 2t + 5

    so v(t) = t^2 + 5t + C

    v(0) = -6 = C

    So v(t) = t^2 + 5t - 6

    We want the distance traveled between t= 0 and t =3

    See the attachment note v(t) < 0 if t <1 so |v(t)| = -v(t) 0<t<1

    and v(t) > 0 for t >1 so |v| = v(t) 1 < t < 3
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