• # question_answer An electron starting from rest has a velocity$v$ that increases linearly with time t as$v=kt,$ where$k=2\text{ }m{{s}^{-2}}$. The distance covered by electron in first 3 s is A)  9m           B)  11 m C)  33m          D)  40m

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       $t=3~$ $\Rightarrow$ $x={{(3)}^{2}}=9m$