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Math Help - Solving this second order?

  1. #1
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    Solving this second order?

    I have the following equation I am using for some air resistance calculations, I want to solve so that v becomes a function of t:

    av^2 + (b/t)v = c

    a, b, and c are constants.

    v = f(t), v = ?...

    I have no idea where to start (I took up through Calc 2 in undergrad). Thanks in advance for your help!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by KwonSau View Post
    I have the following equation I am using for some air resistance calculations, I want to solve so that v becomes a function of t:

    av^2 + (b/t)v = c

    a, b, and c are constants.

    v = f(t), v = ?...

    I have no idea where to start (I took up through Calc 2 in undergrad). Thanks in advance for your help!
    This has nothing to do with Calculus and everything to do with the quadratic formula:
    av^2 + \left ( \frac{b}{t} \right ) v = c

    atv^2 + bv - c = 0

    v = \frac{-b \pm \sqrt{b^2 + 4act}}{2at}

    -Dan
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  3. #3
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    Error

    topsquark,

    You made an error in your work:

    av^2+\left(\frac{b}{t}\right)v=c
    atv^2+bv-ct=0
    (You had atv^2+bv-c=0).

    This changes the answer to:
    v=\frac{-b\pm\sqrt{b^2+4act^2}}{2at}

    -Kevin C.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TwistedOne151 View Post
    topsquark,

    You made an error in your work:

    av^2+\left(\frac{b}{t}\right)v=c
    atv^2+bv-ct=0
    (You had atv^2+bv-c=0).

    This changes the answer to:
    v=\frac{-b\pm\sqrt{b^2+4act^2}}{2at}

    -Kevin C.
    Whoops! Thanks for the catch! (I knew I should have checked the units on that.)

    -Dan
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  5. #5
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    Wow. Thanks for the quick help guys. (I knew it wasn't calc, I just mentioned Calc 2 to show how little math experience I had). I completely forgot about the quadratic equation..dental school hasn't really been testing my algebra skills :/
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