Answer:
Given, dv/dt = - kv3 or\[\text{d}\upsilon
/{{\upsilon }^{\text{3}}}=-\text{kdt}\].
Integrating it within the condition of motion we have
\[\int\limits_{{{v}_{0}}}^{v}{\frac{dv}{{{v}^{3}}}=-\int\limits_{0}^{t}{k\,\,dt}}\] or \[\left(
-\frac{1}{2{{v}^{2}}} \right)_{{{v}_{0}}}^{v}=-k(t)_{0}^{t}\]
or \[\frac{1}{{{v}^{2}}}-\frac{1}{v_{0}^{2}}\]=2kt or v
= \[\frac{{{v}_{0}}}{\sqrt{1+2kv_{0}^{2}t}}\]
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