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  4. An electron starting from rest has a velocity v that increases linearly with time t as v=kt, where k=2ms-2 . The distance covered by electron in first 3 s is

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Q. An electron starting from rest has a velocity $ v $ that increases linearly with time $t$ as $ v=kt, $ where $ k=2ms^{-2}$ . The distance covered by electron in first $3\,s$ is

Rajasthan PETRajasthan PET 2012

Solution:

Given, $ v=kt $
Also $ k=2m{{s}^{-2}} $
$ \therefore $ $ v=2t $
or $ \frac{dx}{dt}=2t $
On integration of both sides
$ x={{t}^{2}}+c $
When, $ t=0, $ then $ x=0 $
$ \therefore $ $ 0={{(0)}^{2}}+c $
$ \Rightarrow $ $ c=0 $
So, we get $ x={{t}^{2}} $
When $ t=3 $
$ \Rightarrow $ $ x={{(3)}^{2}}=9m $