A) \[{{10}^{-4}}kg\,{{m}^{-1}}\]
B) \[{{10}^{-1}}kg\,{{m}^{-1}}{{S}^{-1}}\]
C) \[{{10}^{-3}}kg\,{{m}^{-1}}\]
D) \[{{10}^{-3}}kg\,{{s}^{-1}}\]
Correct Answer: A
Solution :
| [a] \[\frac{1}{2}mv_{f}^{2}=\frac{1}{8}mv_{0}^{2}\] |
| \[{{v}_{f}}=\frac{{{v}_{0}}}{2}=5\,m/s\] |
| \[({{10}^{-2}})\frac{dv}{dt}=-k{{v}^{2}}\] |
| \[\int_{10}^{5}{\frac{dv}{{{v}^{2}}}}=-1000k\int_{0}^{10}{dt}\] |
| \[\frac{1}{5}-\frac{1}{10}=100\,k(10)\] |
| \[k={{10}^{-4}}\] |
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