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Average Speed Computation

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    The problem is in the provided link (it is questions 2.2) http://www.docstoc.com/docs/3817109/Chapter-Problems-A-car-travels-up-a-hill-at-a


    2. Relevant equations



    3. The attempt at a solution
    I understand the duration of time it takes to go up the hill is a larger time interval than going down; but I fail to see that fact as a viable way to justify not just simply adding the to velocities and dividing by two. Could someone please understand this part to me, thank you.
     
  2. jcsd
  3. Feb 20, 2012 #2

    PeterO

    User Avatar
    Homework Helper

    Average speed is total distance / total time. The length of the hill enables us to calculate the time for the trip - and has no other application.

    Perhaps an example is easier explanation.

    Suppose the hill is 10 km long, and you travel up at 10 km/h and down and 30 km/h

    You are tending to an answer of 20 km/h for the average speed.

    The total trip (up then down) is 20km. At 20 km/h that would take 1 hour

    HOWEVER: If travelling at 10km/h on the way up, it takes 1 hour to get up the hill, so it is impossible to get up and down in 1 hour - so to simply add the velocities and divide by 2 doesn't work.

    The simple average only applies if you travel at different speeds for equal times.

    40 kph for 1 hour then 60 kph for 1 hour means an average speed of 50 kph
    Note that you covered 40 km in the first hour then 60 km in the second hour - so it can't have represented a trip in opposite directions along the same piece of road.
     
  4. Feb 21, 2012 #3
    That was bloody brilliant, thank you so very much for taking your time to answer my question.
     
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