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Trouble understanding the answer

  1. Feb 10, 2012 #1
    1. The problem statement, all variables and given/known data
    A person walks in a straight line from point A to point B at a constant speed of 5.00m/s and walks back from point b to point a, with a constant speed at 3.00 m/s. What is the average speed of the entire trip.


    2. Relevant equations



    3. The attempt at a solution
    First, I know how to solve this problem.

    [tex] 5.00m/s = \frac {d}{t_1} [/tex]
    and

    [tex] -3.00 m/s = -\frac{d}{t_2}[/tex]

    Therefore
    [tex] V_avg = \frac{Total Distance}{Total Time}= \frac{d+d}{\frac{d}{5.00m/s}+\frac{d}{3.00m.s}}[/tex]

    Some simple math and we end up with answer of 3.75 m/s

    And that is the answer in the book. The problem is I only got this after I realized my first attempt was wrong and I couldn't figure out why. I tracked down the problem to the simple fact that I didn't write -3.00m/s. I don't particularly understand why it would be -3.00m/s

    The way I thought about this initial was that average speed, the direction doesn't matter since they are not vectors, so when I wrote [tex] 3.00=\frac{d}{t_2} [/tex] it made sense to me. So I guess my question is, why is it negative and not just positive? Maybe i'm just so tired tonight.
     
  2. jcsd
  3. Feb 10, 2012 #2

    jedishrfu

    Staff: Mentor

    Since it says avg speed, you don't use minus 3m/s just 3 m/s

    Distance from a to b is the same as distance from b to a

    (2 * d) / ( t1 + t2 ) = avg speed

    Just sub in for the t values and simplify.

    I think the problem is stated wrong in your book as the minus 3 m/s in the answer implies avg velocity and velocity is direction dependent.
     
  4. Feb 10, 2012 #3
    You know what, I think you just confirmed that my brain was fried because as I reworked it, it became obvious -_-. Now I feel a bit like an idiot. I'll take this as a sign I need sleep.
     
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