A body starts moving with a velocity $v_{0} = 10 {ms}^{- 1}$ . It experiences a retardation equal to $0.2 v^{2}$ . Its velocity after $2 s$ is given by

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$- 2 {ms}^{- 1}$

$+ 4 {ms}^{- 1}$

$+ 6 {ms}^{- 1}$

$+ 2 {ms}^{- 1}$

answer is A.

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Detailed Solution

$a = \frac{d v}{d t} = 0.2 v^{2} ∴ \int_{10}^{v} - 5 v^{- 2} = \int_{0}^{2} d t ∴ {[\frac{5}{v}]}_{10}^{v} = 2 ∴ \frac{5}{v} - \frac{5}{10} = 2 v = 2 m / s$

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