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Average Velocity for a Runner Running Half a Lap

  1. Jan 31, 2016 #1
    1. The problem statement, all variables and given/known data
    A runner covers one lap of a circular track 40.0 min diameter in 62.6 s .

    2. Relevant equations
    If she covered the first half-lap in 28.7 s , what were her average velocity for that half-lap?

    3. The attempt at a solution

    Attempt 1:
    Initial Distance: 0 m
    Distance of a half-lap: 20π m
    Initial Time: 0 s
    Final Time: 28.7 s

    Displacement = Δx/Δt, where Δx = xf - x0
    Displacement = (20π m - 0 m)/28.7 s = 2.19 m/s

    Attempt 2:
    By inspection, her total distance is aligned original position, making Δx = 0, thereby making displacement = 0.
     
  2. jcsd
  3. Jan 31, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Displacement is a distance. So that corresponds to your Δx, the distance between the starting location and the final location. Note that the actual path followed between the start and end points is irrelevant. Only the separation between the start and end matter.

    Average velocity is the displacement divided by the time it took. So ##V_{avg} = Δx/Δt##.
     
  4. Jan 31, 2016 #3
    Except for using 'displacement' when you mean 'speed', #1 looks fine.

    #2 : Not sure what you are positing here. What does 'aligned' mean?
    She went 1/2 way around a circular track so ends up on the opposite side.

    What is the question?
     
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