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Homework Help: Finding the units in an algebraic equation for velocity

  1. Dec 28, 2017 #1
    1. The problem statement, all variables and given/known data
    During a short interval of time the speed v in m/s of an automobile is given by v = at^3 + bt^4 , where the time t is in seconds. The units of a and b are respectively:
    (a) m⋅s^2 ; m⋅s^4 (b) s^3/m; s^4/m (c) m/s^2 ; m/s^3 (d) m/s^3 ; m/s^4 (e) m/s^4 ; m/s^5

    2. Relevant equations
    None


    3. The attempt at a solution
    I have not a single clue, and I'm assuming that there is a trick to this that I'm not getting. I know that the velocity is measured in m/s, but I don't understand how finding the units of a and b is even possible.
     
  2. jcsd
  3. Dec 28, 2017 #2

    gneill

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    Staff: Mentor

    What do you know about the relationship between the units of terms in an equation where you are summing the terms? Can you add apples to oranges? :smile:
     
  4. Dec 28, 2017 #3
    Nope, I know that you can only add apples to apples, or oranges to oranges, which means that both a and b need to be measured with the same units. Since this is an equation for velocity, I would assume that the units of the right hand side would also need to be m/s.
     
  5. Dec 28, 2017 #4

    gneill

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    Staff: Mentor

    Think again. The terms also contain powers of t. What are the units associated with t?
    Right. So you need to choose the units of a and b so that their terms (including their t's) both work out to m/s.
     
  6. Dec 28, 2017 #5
    So, I'm looking for units of a and b for which all of the s's in the numerator cancel, and there is only one s left in the denominator, and one m in the numerator?
     
  7. Dec 28, 2017 #6

    gneill

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    Staff: Mentor

    Sounds like a plan!
     
  8. Dec 28, 2017 #7
    Thank you!
     
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