Average Velocity for a Runner Running Half a Lap

[in the rye]

Homework Statement

A runner covers one lap of a circular track 40.0 min diameter in 62.6 s .

Homework Equations

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

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.

 

[gneill]

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 $V_{avg} = Δx/Δt$.

 

[alw34]

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?