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Math Help - Speeding up with a given function

  1. #1
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    Speeding up with a given function

    A car's position is given by d(t)=2t^3-24t^2+78t-56, find when it is speeding up and speeding down.

    I'm a little confused if it means the acceleration (2nd derivative) or velocity (1st derivative). I'd have thought acceleration, but the 2nd derivative is only positive when t>4, but when looking at its graph (http://www.wolframalpha.com/input/?i=2x^3-24x^2%2B78x-56), you' assume it was speeding up after it hit its maximum value until the inflection point.

    Was I right for thinking it speeds up after it hit the max/min?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by youngb11 View Post
    A car's position is given by d(t)=2t^3-24t^2+78t-56, find when it is speeding up and speeding down.

    I'm a little confused if it means the acceleration (2nd derivative) or velocity (1st derivative). I'd have thought acceleration, but the 2nd derivative is only positive when t>4, but when looking at its graph (http://www.wolframalpha.com/input/?i=2x^3-24x^2%2B78x-56), you' assume it was speeding up after it hit its maximum value until the inflection point.

    Was I right for thinking it speeds up after it hit the max/min?
    The term "speeding up" refers to an increasing speed. Thus you are looking for a region of the graph where |v| is increasing. Similarly for "speeding down" you are looking for when |v| is getting smaller.

    Mathematically speaking take the derivative of your displacement function to get the velocity. Then find
    \displaystyle a = \frac{d|v(t)|}{dt}

    -Dan
    Last edited by topsquark; March 23rd 2011 at 05:02 PM.
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by topsquark View Post

    Mathematically speaking integrate your displacement function to get the velocity. Then find
    \displaystyle a = \frac{d|v(t)|}{dt}

    -Dan
    Integrate the displacement function to find velocity?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by e^(i*pi) View Post
    Integrate the displacement function to find velocity?
    (hangs his head in shame)

    Thanks for the catch. I have fixed it in my post.

    -Dan
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