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  4. Consider a machine delivering power to a body which is proportional to velocity of the body. Suppose the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to (choose the correct option from the following) :-

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Q. Consider a machine delivering power to a body which is proportional to velocity of the body. Suppose the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to (choose the correct option from the following) :-

NTA AbhyasNTA Abhyas 2020

Solution:

Power $=Fv \, \propto v$
$\Rightarrow \, mv\frac{d v}{d t}=kv,$ where $k= \, $ constant
$\Rightarrow \, m \, dv.dt=k \, \Rightarrow \, \, \, mv\frac{d v}{d x}=k$
$\Rightarrow \, \, vdv=\frac{k d n}{m}$