How to find displacement of 400m track

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SUMMARY

The displacement of a runner completing 6.5 laps around a 400m track is 160m, not 200m as initially thought. Displacement is defined as the shortest distance from the starting point to the endpoint, which in this case is influenced by the track's curvature. The misunderstanding arose from not considering the track's shape and the runner's starting position. A diagram accompanying the question clarified the correct displacement measurement.

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  • Understanding of basic physics concepts, specifically displacement and distance.
  • Familiarity with the geometry of circular tracks.
  • Ability to interpret diagrams related to motion and displacement.
  • Knowledge of how to calculate distances based on given parameters.
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  • Study the principles of displacement versus distance in physics.
  • Learn how to analyze motion on circular paths, including concepts like angular displacement.
  • Explore the impact of starting positions on displacement calculations.
  • Review examples of similar problems involving circular tracks and displacement measurements.
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Homework Statement



I know this is basic but I'm stumped

Homework Equations



a runner runs 6.5 laps around a 400m track, what's the displacement. I thought it would be 200m but the answer provided says 160m and I just can't work out how to get to this answer

The Attempt at a Solution

 
Last edited:
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You might need some more details about the shape of the track and the runner's starting point.
 
Displacement will equal the length of the shortest line possible drawn from the starting point to the ending point. As you can see, if the track has any curvature at all during that half of a lap, the displacement will be less than 200 m.
 
Thanks people for your help. However I'm an idiot! Just realized there was a diagram with the question and the displacement marked in...
 

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