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Differentiating with units ?

  1. May 2, 2010 #1
    okay we know that velocity is in meters per second and that acceleration is in
    m/(s^2) , so if I take the derivative of velocity with respect to time i get acceleration .
    but just looking at the units , if i start with velocity m/s (ms^-1) this might sound crazy but can i just take the derivative of s and get -ms^(-2) , any help would be appreciated.
     
  2. jcsd
  3. May 2, 2010 #2

    sylas

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    The units of X/Y are the same as the units of -X/Y. The factor has -1 has no dimension.

    Cheers -- sylas
     
  4. May 2, 2010 #3
    so what i did was correct , except for the minus sign .
     
  5. May 2, 2010 #4

    sylas

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    Yes. When you obtain the units for a differentiation, you just need to do division. The units of X/Y are the same as the units of dX/dY. If you do a full differentiation and then extract units from the result you will get the same result as simply extracting the units by getting units for X and units for Y, and dividing. Actually carrying out a differentiation is overkill if all you want is units, but it gives the same result.

    Cheers -- sylas
     
  6. May 2, 2010 #5
    so we are just dividing everything by dY , in our case s , in all of my physics classes it was never really explained so thanks for taking the time to explain it.
     
  7. May 3, 2010 #6

    sylas

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    You're welcome. Remember that dX/dY is defined as the limit of ΔX/ΔY as the small delta changes go towards 0. Taking a limit makes no difference to the units, so the units of the derivative is indeed the units of a division.
     
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