A car of mass m is traveling at a slow velocity V₀ . It is subjected to a drag resistance of the wind which is proportional to its velocity, the constant of proportionality being k. The distance covered by the car before its speed becomes half is___ _

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$\frac{{mv}_{0}}{4 k}$

$\frac{{mv}_{0}}{2 k}$

$\frac{2 {mv}_{0}}{k}$

$\frac{{mv}_{0}}{k}$

answer is C.

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Detailed Solution

$\begin{array}{l} a = \frac{F}{m} = \frac{kv}{m} \\ or - v \frac{dv}{ds} = \frac{kv}{m} \\ or \int_{v_{0}}^{v_{0} / 2} dv = - \frac{k}{m} \int_{0}^{s} ds \end{array}$
Or S

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