A particular of mass m and charge q starts moving from the origin under the action of an electric field $\overrightarrow{E}=E\stackrel{\wedge }{i}$ and magnetic field $\overrightarrow{B}=B\stackrel{\wedge }{i}$ with a velocity $\overrightarrow{\upsilon }={\upsilon }_0\stackrel{\wedge }{j}$ .The speed of the particle becomes $2{\upsilon }_0$ after time t. then t equals

Since $\overrightarrow{E}$ and $\overrightarrow{B}$ are parallel to each other and $\overrightarrow{\upsilon }$  is perpendicular to both, so, the path of the particle is a helix of increasing pitch. The speed of particle at any time t is $\upsilon =\sqrt{{\upsilon }_x^2+{\upsilon }_y^2+{\upsilon }_z^2}\mathrm{...........}\left(1\right)$
Since the magnetic force acts along -z axis, so the particle will have a circular track in yz plane, where  ${\upsilon }_y^2+{\upsilon }_z^2={\upsilon }_0^2$
Due to the electric field along the x-axis, the x velocity of the particle keeps on increasing with time t as
${\upsilon }_x^{ }=\left(\frac{qE}{m}\right)t$      $\{\therefore a=\frac{qE}{m}\}$                                         
According to the problem, we have  $\upsilon =2{\upsilon }_0$
Substituting the values in equation (1), we get
$t=\sqrt{3}\left(\frac{m{\upsilon }_0}{qE}\right)$