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Thread: Differentiation(average speed)

  1. #1
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    Differentiation(average speed)

    I'm not sure about this so a bit of help would be great.

    Determine the average speed given that the distance travelled, $\displaystyle s$, in metres, relative to time, $\displaystyle t$, in seconds is $\displaystyle s(t)=2t^2 + 1$, between $\displaystyle t=2$ and $\displaystyle t=4$

    Do I first do the first derivative of $\displaystyle s(t)=2t^2 + 1$ to get the equation for the speed at a point and then substitute in $\displaystyle t=2$ and $\displaystyle t=4$, and then use those values returned to get the gradient between the 2 points?
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  2. #2
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    Quote Originally Posted by MarcoMP View Post
    I'm not sure about this so a bit of help would be great.

    Determine the average speed given that the distance travelled, $\displaystyle s$, in metres, relative to time, $\displaystyle t$, in seconds is $\displaystyle s(t)=2t^2 + 1$, between $\displaystyle t=2$ and $\displaystyle t=4$

    Do I first do the first derivative of $\displaystyle s(t)=2t^2 + 1$ to get the equation for the speed at a point and then substitute in $\displaystyle t=2$ and $\displaystyle t=4$, and then use those values returned to get the gradient between the 2 points?
    Avarage speed $\displaystyle = \frac{s(4) - s(2)}{4 - 2}$.
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    Quote Originally Posted by mr fantastic View Post
    Avarage speed $\displaystyle = \frac{s(4) - s(2)}{4 - 2}$.
    So I take it I don't have to do the average speed between the 2 points while using the instantaneous speed?
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  4. #4
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    You would only need to use differetiation if you were given the model for distance as

    $\displaystyle \frac{d}{dt}(d(t)) = s(t) $

    then substitiute in those values as the previous poster suggested.

    Quote Originally Posted by MarcoMP View Post
    So I take it I don't have to do the average speed between the 2 points while using the instantaneous speed?
    I agree as the average between 2 points is never instantaneous.
    Last edited by mr fantastic; May 3rd 2009 at 01:52 AM. Reason: Merged posts
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  5. #5
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    Quote Originally Posted by MarcoMP View Post
    So I take it I don't have to do the average speed between the 2 points while using the instantaneous speed?
    If you had to do that I would have said so.
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