Given,

Power delivered by the engine $P=1 \mathrm{J} {\mathrm{s}}^{-1}$

Mass of the body is $m= 2 \mathrm{kg}$ 

Body starts from the rest, $u=0$

Using work energy Theorem, 

$W=∆K=Pt$

$Pt=\frac{1}{2}m{v}^2-0$

Substitute the values in the above equation, we get
$\left(1\right)t=\frac{1}{2}\times 2\times v^2$
$\Rightarrow v=\sqrt{t}=\frac{\mathrm{d}s}{\mathrm{d}t}$
$\Rightarrow {\int }_0^{t}ds={\int }_0^9\sqrt{t}dt$

$\Rightarrow s=\frac{{\left(9\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=\frac{2}{3}\times 27$

$\Rightarrow s=18 \mathrm{m}$