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Dimensional analysis - working out if this is dimensionally correct

  1. Jul 26, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm trying to work out if the following is dimensionally correct. I think I'm getting stuck at the (x - x0)

    hD7pb.jpg

    2. Relevant equations

    In this case v is velocity (L/T), a is acceleration (L/T²), and x represents displacement, which is a length (L)

    3. The attempt at a solution

    My attempt was such:

    v² = v0² = (L/T)² or L²/T²

    a = L/T²

    (x - x0) confuses me. That would work out to (L - L), correct? So a(x - x0) = L/T²(L - L)

    Don't (L - L) cancel out, leaving me just with L/T² which is NOT the same as L²/T²?

    According to the sheet, this expression is supposed to be dimensionally correct. Any pointer appreciated.
     
  2. jcsd
  3. Jul 26, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Hi ulfy1, welcome to PF!

    The difference between two lengths is length. Just think, what you get when you cut a 2 meter long piece from a 10 m long string. You get a piece of 8 meter length.

    ehild
     
  4. Jul 26, 2012 #3
    Ah, I think I got it! I have to get that dimensions are just that, dimensions.

    So in truth, a(x - x0) is really just L/T²(L) which is L²/T²

    I think that's the right conclusion and makes the expression correct.

    Thanks!
     
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