A particle describes a semi circle of radius 14 cm. What is its distance and displacement?

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There is a difference between distance traveled and displacement. Distance means the total length of travel of an object, while displacement is the difference in position between where an object starts and where it finishes.

For the distance a particle travels around a semi circle, you would use the formula for circumference of a circle, and divide that in half to account for the fact that it has traveled half way around. The formula is 2 pi r for the circumference; the distance half way around is pi r, so for your example, the particle travels pi times 14 cm, or approximately 44 cm.

The displacement of your particle would be the diameter of your circle--it ends up in the same place as when you calculated distance, but the change in its position is 28 cm, or 2 times the radius.

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