A particle has an initial velocity of $3\widehat{i}+4\widehat{j}$ and an acceleration of  $4\widehat{i}+3\widehat{j}$. Then its speed in 10s is…..

Given initial velocity  $\overline{u}=3\widehat{i}+4\widehat{j}$
Acceleration  $\overline{a}=4\widehat{i}+3\widehat{j}$
Time t=10s.
$\therefore$ from equation  $\overline{V}=\overline{u}+\overline{a}t$
$\begin{array}{l}\overline{V}=(\widehat{3}+4\widehat{j})+(4\widehat{i}+3\widehat{j})10\\ =(3\widehat{i}+4\widehat{j})+(40\widehat{i}+30\widehat{j})\\ =43\widehat{i}+34\widehat{j}\end{array}$  
$\therefore$ Magnitude of velocity (or) speed
$\begin{array}{l}V=\sqrt{\left({43}^2\right)+(34{)}^2}\\ =\sqrt{1849+1156}\\ =\sqrt{3005}=54.82\mathrm{m}/\mathrm{s}\end{array}$