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Question

An object travels around a circle of radius 6 m with speed 3π ms1. Find the distance and displacement after 3 s.

A
9π m, 62 m
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B
9π m,0 m
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C
12π m,62 m
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D
12π m,0 m
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Solution

The correct option is A 9π m, 62 m
Given:
Radius of the circle, r=6 m
Time taken, t=3 s
Speed, v=3π ms1
Distance travelled is the product of speed and time.
d=3π×3=9π m
Circumference, C=2πr=12π m
In 3s it would have travelled,
d3=9π12π=(34)th of the circle.
We know, displacement is the shortest distance between initial and final points.
Since the object covers (34)th of the circle), the object starts its journey from point A and ends its journey at point B.
Therefore, displacement of the object is AB.
AB=AO2+OB2
AB=62+62 (using Pythagoras theorem)
AB=62 m

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