A cyclist moving on a level road at 4 m/s stops pedalling and free wheels to rest. The retardation of the cycle has two components, a constant 0.08 m / s 2 due to friction in the working parts, and re

Question

A cyclist moving on a level road at 4 m/s stops pedalling and free wheels to rest. The retardation of the cycle has two components, a constant 0.08 m / s 2 due to friction in the working parts, and resistance of 0.02 v 2 m / s 2 where v is speed in meter per second. The distance traversed by the cycle before it comes to rest (approximately) is

TestHub · Accepted Answer

Let x be the displacement of the particle; v = d t d x ​ and retardation a = d t d v ​ = v d x d v ​ Retardation = 0.08 + 0.02 v 2 = 0.02 ( 4 + v 2 ) v d x d v ​ = − 0.02 ( 4 + v 2 ) ⇒ ∫ 0 x 1 ​ ​ d x = − ∫ 4 0 ​ 0.02 ( 4 + v 2 ) v ​ d v ⇒ x 1 ​ = 0.04 1 ​ lo g 5 ≈ 40 4 1 ​ mts

Mathematics - Application of Derivative Question with Solution | TestHub

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