A) \[{{f}^{2}}\]
B) \[{{f}^{3}}\]
C) \[-{{f}^{3}}\]
D) \[-{{f}^{2}}\]
Correct Answer: B
Solution :
\[t=\frac{{{v}^{2}}}{2}\Rightarrow {{v}^{2}}=2t\Rightarrow 2v\frac{dv}{dt}=2.\] \[\Rightarrow \frac{dv}{dt}=\frac{1}{v}=f\Rightarrow \frac{df}{dt}=-\frac{1}{{{v}^{2}}}\frac{dv}{dt}=-\frac{1}{{{v}^{2}}}\times \frac{1}{v}\] \[\Rightarrow -\frac{df}{dt}=\frac{1}{{{v}^{3}}}={{f}^{3}}\].
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