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Homework Help: Acceleration and speed as m*s^-1

  1. Jan 23, 2014 #1
    I was given this question today and I have never seen acceleration or speed with a minus power in the unit (m/s^-2). Also speed in the question has a ^-1 in the unit and I thought the unit for speed was m/s (meters per second)

    1. The problem statement, all variables and given/known data

    A body starts from rest and is subject to a constant contant acceleration of 4ms^-2 up to a speed of 20ms^-1. It then travels 20ms^-1 for 30 seconds after witch time it is retarded to a speed of 4ms^-1, if the complete motion takes 50 seconds, Find:

    A) The time taken to reach 20ms^-1.

    B) The retardation.

    C)Total distance travelled.

    2. Relevant equations

    3. The attempt at a solution

    I have know idea what these strange units mean.
  2. jcsd
  3. Jan 23, 2014 #2


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    Staff: Mentor

    Hi Xecutive. Welcome to PF!

    It is simply standard algebra applied to units (which should be treated as mathematical objects).

    $$x^{-1} = \frac{1}{x}$$

    $$\mathrm{m} \; \mathrm{s}^{-1} = \frac{\mathrm{m}}{\mathrm{s}}$$

    $$\mathrm{m} \; \mathrm{s}^{-2} = \frac{\mathrm{m}}{\mathrm{s}^2}$$

    Note that it is not ##\mathrm{m} / \mathrm{s}^{-1}##, but ##\mathrm{m} \; \mathrm{s}^{-1}##. The former would give
    \mathrm{m} / \mathrm{s}^{-1} = \frac{\mathrm{m}}{\mathrm{s}^{-1}} = \mathrm{m} \; \mathrm{s}
  4. Jan 23, 2014 #3


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    Science Advisor
    Homework Helper
    Gold Member

    you mean ms^-2 not m/s^-2
    yes, the unit for speed is m/s, and m/s can be writen as ms^-1.....it's just taking the denominator, s, and placing it in the numerator as s^-1.
    I personally would rather see it written as m/s instead of ms^-1, but they are nevertheless mathematically the same unit, just an algebraic manipulation of the variables.

    Welcome to these forums!
  5. Jan 23, 2014 #4
    It seems so obvious now.

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