Given initial velocity, $u=5 \times 10^{4} \,ms ^{-1}$

And acceleration, $a=10^{4} \,ms ^{-2}$

$(i)$ final velocity $=v=2 u=2 \times 5 \times 10^{4} \,ms ^{-1}=10 \times 10^{4}\, ms ^{-1}$

To find $t,$ use $v=u+a t$

Or $t=\frac{v-u}{a}$

$\left(\frac{10 \times 10^{4}-5 \times 10^{4}}{10^{4}}\right)=\frac{5 \times 10^{4}}{10^{4}}=5 \,s$

$(ii)$ Using $s=u t+\frac{1}{2} a t^{2}$

$=\left(5 \times 10^{4}\right) \times 5+\frac{1}{2}\left(10^{4}\right) \times(5)^{2}=25 \times 10^{4}+\frac{25}{2} \times 10^{4}=37.5 \times 10^{4}\, m$