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What dimensions of (time)−2 mean ?

  1. Jan 3, 2016 #1
    I am self learning Physics From a course I read the following :
    " .. d^2x/dt^2 = -k/m x The left hand side is an acceleration so k/m must have dimensions of (time)−2 .. "
    I understand that the left hand is acceleration but why does it imply that k/m must have dimensions of (time)−2 ? I guess I also don't understand the meaning of "dimensions" here. Thank you very much.
  2. jcsd
  3. Jan 3, 2016 #2


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    Staff: Mentor

    Google for "dimensional analysis" - this is something you'll have to learn very early in your self-study.
  4. Jan 3, 2016 #3


    Staff: Mentor

    Dimensional analysis and units are one of the most important things you can learn. If you always check your units you will catch a lot of mistakes.

    In a system of units, each unit is considered to have some dimension. For example, in the SI system the meter (m) has the dimension of length (L) and the second (s) has the dimension of time (T).

    So what are the SI units and dimensions for acceleration?
  5. Jan 3, 2016 #4
    Thank you very much for your help, I really appreciate ! I understand now that length / time squared are the dimensions of acceleration and its SI units are m / s squared
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