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Simple velocity question

  1. Sep 17, 2015 #1
    1. The problem statement, all variables and given/known data

    A car makes a trip due north for three-fourths of the time and due south one-fourth of the time. The average northward velocity has a magnitude of 27 m/s, and the average southward velocity has a magnitude of 17 m/s. What is the average velocity (magnitude and direction) for the entire trip?

    2. Relevant equations

    ##\displaystyle v_{avg} = \frac{x}{t}##

    3. The attempt at a solution

    ##\displaystyle v_{avg} = \frac{x}{t} = \frac{v_1t_1 + v_2t_2}{t} = \frac{v_1(\frac{3}{4}t) + v_2(\frac{1}{4}t)}{t} = \frac{3}{4}v_1 + \frac{1}{4}v_2 = \frac{3}{4}27 + \frac{1}{4}(-17) = +16~m/s##

    Is this the correct answer for the average velocity over the whole trip? If not, what am I doing wrong?
     
    Last edited: Sep 17, 2015
  2. jcsd
  3. Sep 17, 2015 #2

    jbriggs444

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    Is the southward velocity 7 or 17?
     
  4. Sep 17, 2015 #3
    Oops, it's 17 m/s. I fixed it.
     
  5. Sep 17, 2015 #4

    jbriggs444

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    In that case, your work looks correct.

    Edit: The question asks for magnitude and direction rather than a signed result.
     
  6. Sep 17, 2015 #5
    Alright, I'll take that into account. Thanks!
     
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