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How to tell which function has distance proportional to time?

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data

    http://imgur.com/aYCc9

    also in attachment

    2. Relevant equations

    n/a

    3. The attempt at a solution

    I'm not sure how to tell when distance is proportional to time. My guess is it would be graphs a and b because they're both straight lines and when time increases, distance increases a set amount as well.

    Also can you explain why the curve function does not have distance proportionate to time?
     

    Attached Files:

  2. jcsd
  3. Sep 10, 2012 #2

    CWatters

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    a) Curve A and B show distance as a linear function of time.

    b) I believe only curve A shows distance proportional to time. Curve B does not pass through the origin. Curve C isn't straight.

    Regarding Curve C. The expression "in proportion" hints at constant ratio. So for it to be directly proportional the equation must be of the form

    y/x = k
    or
    y = kx

    where k is a constant called the constant of proportionality. K can be -ve or +ve.
     
    Last edited: Sep 10, 2012
  4. Sep 10, 2012 #3

    CWatters

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    See above. In addition, for this particular example only, on the right hand side the distance appears to be increasing while time remains constant. Putting aside the practicalities of achieving infinite velocity it shows that in this region of the curve distance appears to be independant of time.
     
  5. Sep 10, 2012 #4

    CWatters

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    The expression "proportional to time" is normally taken to mean "proportional to time1 and excludes other powers such as timen, time1/n etc
     
  6. Sep 10, 2012 #5
    Thanks everyone for the replies. I got it now.
     
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