Duration: 10:48

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A cyclist moving on a level road at \( 4 \mathrm{~m} / \mathrm{s} \) stops pedalling and lets the wheels come to rest to rest. The retardation of the cycle has two components; a constant \( 0.08 \mathrm{~m} / \mathrm{s}^{2} \) due to friction in the working parts and resistance of \( 0.02 \mathrm{v}^{2} / \mathrm{m} \) where \( v \) is speed in metres per second. What distance is traversed by the cycle before it comes to rest? (Consider \( \ln 5=1.61) \)
(A) \( \frac{171}{2} \) metres
(B) \( \frac{161}{4} \) metres
(C) \( \frac{161}{8} \) metres
(D) None of these
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