Applications Of Derivatives Question 313
If $ t=\frac{v^{2}}{2} $ ,then $ ( -\frac{df}{dt} ) $ is equal to, (where f is force)
[MP PET 1991]
Options:
A) $ f^{2} $
B) $ f^{3} $
C) $ -f^{3} $
D) $ -f^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ t=\frac{v^{2}}{2}\Rightarrow v^{2}=2t\Rightarrow 2v\frac{dv}{dt}=2\frac{dv}{dt} $
$ \Rightarrow \frac{dv}{dt}=\frac{1}{v}=f\Rightarrow \frac{df}{dt}=-\frac{1}{v^{2}}\frac{dv}{dt}=-\frac{1}{v^{3}} $
$ \Rightarrow -\frac{df}{dt}=\frac{1}{v^{3}} $
BETA
