Displacement around a 400m track

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SUMMARY

A runner completing 6.5 laps around a 400m track in 12 minutes has a displacement of 160m from the starting point. The total distance covered is 2.6km, resulting in an average speed of 3.61m/s. The confusion arises from miscalculating the displacement based on the runner's position on the track, as the correct displacement accounts for the track's layout and the runner's final position relative to the start. Understanding the geometry of the track is essential for accurately determining displacement.

PREREQUISITES
  • Understanding of basic kinematics
  • Familiarity with displacement versus distance concepts
  • Knowledge of circular motion and track geometry
  • Ability to perform basic calculations involving speed and distance
NEXT STEPS
  • Study the principles of displacement in circular motion
  • Learn how to calculate displacement on different geometric shapes
  • Explore kinematic equations for motion in one and two dimensions
  • Investigate the effects of track layout on running performance
USEFUL FOR

Students studying physics, runners analyzing their performance, and educators teaching concepts of motion and displacement.

bionut
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Homework Statement



A runner completes 6 1/2 laps around a 400m track during 12min reun test. What is the runners displacement at the end of the 12 min?

Homework Equations





The Attempt at a Solution



Well the distance covered is 2.6km or 2600m in 720s, avg speed = 3.61m/s

So I calculated the dispalcement to be: 200m, because he is 200m from his inital position, but the correct answer is 160m is anyone able to help?
 
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bionut said:

Homework Statement



A runner completes 6 1/2 laps around a 400m track during 12min reun test. What is the runners displacement at the end of the 12 min?

Homework Equations





The Attempt at a Solution



Well the distance covered is 2.6km or 2600m in 720s, avg speed = 3.61m/s

So I calculated the dispalcement to be: 200m, because he is 200m from his inital position, but the correct answer is 160m is anyone able to help?

Suppose the running track was actually a 100m square. If he started in one corner and finished in the opposite corner , he would be 141.2 m away.
If he started in the middle of one side, he would finish in the middle of the other side - a mere 100m away.
It would appear that on a standard running track, the 200m start is 160m displaced from the finish - back along the straight then around the bend.
I hope your problem gave sufficient detail of the track to get the definitive 160m answer.
 

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