Average Velocity for a Runner Running Half a Lap

In summary, the conversation discusses a runner's average velocity for half a lap on a circular track. Two attempts are made to find the average velocity, with the first attempt using the formula for displacement and the second attempt considering the runner's position on the track. The conclusion is that the average velocity is equal to the displacement divided by the time it took.
  • #1
in the rye
83
6

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.
 
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  • #2
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##.
 
  • #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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Related to Average Velocity for a Runner Running Half a Lap

1. What is the formula for calculating average velocity for a runner running half a lap?

The formula for average velocity is distance divided by time. For a runner running half a lap, the distance would be half of the lap length and the time would be the time it takes to complete half a lap.

2. How does average velocity differ from average speed?

Average velocity takes into account the direction of motion, while average speed only considers the magnitude of motion. For a runner running half a lap, their average velocity would be the displacement divided by the time, while their average speed would be the total distance covered divided by the time.

3. Is average velocity affected by the runner's starting position?

No, average velocity is not affected by the runner's starting position. It only considers the displacement and time, regardless of where the runner started.

4. How can average velocity be used to improve a runner's performance?

Average velocity can be used to track a runner's progress and identify areas for improvement. By calculating their average velocity for each half lap, a runner can work on increasing their speed or maintaining a consistent velocity to improve their overall performance.

5. Can average velocity be negative?

Yes, average velocity can be negative if the runner's displacement is in the opposite direction of their initial position. For example, if a runner starts at the 100m mark and finishes at the 50m mark, their average velocity would be negative as they moved in the negative direction (towards the start line).

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