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Thread: Quadratic word problem

  1. #1
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    Quadratic word problem

    The distance, d (in metres), which an object travels. is given by the equation $\displaystyle d=ut-8t^2 $ where u is the initial velocity (in metres per second) and t is the time in seconds it has been travelling. Show that there is only one value for t when $\displaystyle u^2 =32d$

    I'm having real trouble solving this equation for t using any algebraic method that I've learnt for quadratic equations.
    I can't figure out how to put it into the quadratic formula simply for the fact that i can't get any of the variables by themself on either side of the equation to set as x.

    The steps I've tried so far in order to rearrange for t are:
    $\displaystyle d=ut-8t^2$
    add 8t^2 to both sides
    $\displaystyle d+8t^2=ut$
    divide both sides by t
    $\displaystyle d/t+8t=u$
    take d/t away from both sides
    $\displaystyle 8t=u-d/t$
    and here is where i lose track, because i figure out that i can't rearrange for t at all. i've considered converting d/t into V (final velocity) but i can't see that helping much.
    Any suggestions would be much appreciated.
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  2. #2
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    Quote Originally Posted by mattty View Post
    The distance, d (in metres), which an object travels. is given by the equation $\displaystyle d=ut-8t^2 $ where u is the initial velocity (in metres per second) and t is the time in seconds it has been travelling. Show that there is only one value for t when $\displaystyle u^2 =32d$

    .
    Rearrange the expression for $\displaystyle d$:

    $\displaystyle
    8t^2-ut+d=0
    $

    This is an equation relating $\displaystyle t,\ u$ and $\displaystyle d$ .

    If for some particular $\displaystyle d$ and $\displaystyle u$ we wish to solve for $\displaystyle t$ we will use the quadratic formula. Now the discriminant for the quadratic is:

    $\displaystyle
    D=u^2-32d
    $

    and it is well known that we have no real roots for $\displaystyle t$ if $\displaystyle D<0$, two real roots if $\displaystyle D>0$, and exactly one real root if $\displaystyle D=0$.

    The last condition above is the one applicable here.

    .
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  3. #3
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    Many thanks for this, apparently maths at 3am isn't my strong point
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