A) 2s
B) 4s
C) 8s
D) 1s
Correct Answer: A
Solution :
\[\frac{dv}{dt}=-2.5\sqrt{v}\Rightarrow \frac{dv}{\sqrt{v}}=2.5dt\] \[\text{Integrating, }\int\limits_{6.25}^{0}{{{v}^{\frac{-1}{2}}}}dv=-2.5\int\limits_{0}^{t}{dt}\] \[\Rightarrow \left[ \frac{{{v}^{+\frac{1}{2}}}}{\left( {}^{1}/{}_{2} \right)} \right]_{6.25}^{0}=-2.5\left[ t \right]_{0}^{t}\] \[\Rightarrow -2{{\left( 6.25 \right)}^{{}^{1}/{}_{2}}}=-2.5t\Rightarrow t=2\text{ sec}\]
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