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Simple Error Analysis Problem

  1. Apr 7, 2005 #1
    I'm having a problem with something I know should be simple, but my answer is off so I'm doing something wrong.

    I need to find the amount of error for an acceleration that was found using the formula a=2d/t^2. Where d represents distance travelled. There is no uncertainty in the distance measurement, only the time.

    Could someone please help.
     
  2. jcsd
  3. Apr 7, 2005 #2

    dextercioby

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    [tex]\Delta a=\left|\Delta \left(\frac{2d}{t^{2}}\right)\right| =4dt^{-3} \Delta t[/tex]

    Daniel.
     
  4. Apr 7, 2005 #3

    xanthym

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    Just in case you're also interested in the SIGN of the error "Δa" in "a" for a given error "Δt" in "t":

    [tex] 1: \ \ \ \ \Delta a \ = \ \Delta \left(\frac{2d}{t^{2}}\right) \ = \ \left ( \frac{\color{red} \mathbf{-} \color{black} 4d}{t^{3}} \right ) \Delta t [/tex]


    ~~
     
  5. Apr 7, 2005 #4

    dextercioby

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    There are no such things as negative errors.Errors always add...

    I'm not interested in that minus...

    Daniel.
     
  6. Apr 7, 2005 #5
    Yes, reported errors are standard deviations (or they should be), and hence are always positive (the definition of standard deviation of [itex]X[/itex] is [itex]\sqrt{\mbox{Var} X}[/itex]).
     
  7. Apr 7, 2005 #6

    xanthym

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    The term "error" alone can be ambiguous. "Standard Deviation" and "Variance" are much more specific, and they are always positive and always "add":

    [tex] 1: \ \ \ \ \ \ \ \color{blue}\mbox{Var(a)}\color{black} \ = \ \overline { \left ( \Delta a \right )^{2}} \ = \ \overline{ \left ( \Delta \left(\frac{2d}{t^{2}}\right) \right )^{2} }\ = \ \left ( \frac{-4d}{t^{3}} \right )^{2} \overline{ \left ( \Delta t \right )^{2} } \ \ + \ \ \left ( \frac{2}{t^{2}} \right )^{2} \overline{ \left ( \Delta d \right )^{2} } [/tex]

    [tex] : \hspace{9cm} \left ( For \ \ \overline{\Delta a} = \overline{\Delta t} = \overline{\Delta d} = \overline{\Delta t \Delta d} = 0 \right ) [/tex]

    [tex] 2: \ \ \ \ \color{red}(\mbox{Standard Deviation})\color{black} \ = \ +\sqrt{\color{blue} \mbox{Var(a)}} [/tex]


    The question here is what the OP had in mind. (We don't know what the OP originally meant by the term in Msg #1.) You :wink: may not be interested in the (-) sign, but the OP might have been ... thus the clarification in Msg #3.


    ~~
     
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