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Question

A person is running on a horizontal circular track of radius R. In the first round, he runs with speed v and takes time t. If he takes time 2t covering the same track in the second round, then his speed will be
(i) v2
(ii) 2v
(iii) πRt
(iv) πRt

A
(i) and (iv)
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B
(ii) and (iv)
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C
(i) and (iii)
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D
(ii) and (iii)
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Solution

The correct option is C (i) and (iii)
For first round:
Radius of circular track = R
Time taken by the person to complete the first round = t
Speed, v=Distance coveredTime taken
Distance covered by the person, s = circumference of circular track = 2πR
v=2πRt
For second round:
Let the new speed of the person be v′.
Distance, s = 2πR
Time, t=2t
v=st
v=2πRt
v=12(2πRt)=πRt
v=v2 (v=2πRt)
Hence, the correct answer is option (b).

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