Given data

• Mass of body: $m = 2\,\text{kg}$
• Constant power delivered: $P = 1\,\text{J/s} = 1\,\text{W}$
• Initial speed: $u = 0$
• Time: $t = 9\,\text{s}$

Use the relation between power and kinetic energy

Since the engine delivers constant power, $P = \frac{d}{dt}\left(\frac{1}{2}mv^2\right)$

With $m=2$ kg, $P = \frac{d}{dt}\left(\frac{1}{2}\cdot 2 \cdot v^2\right) = \frac{d}{dt}(v^2)$

Given $P=1$, $\frac{d}{dt}(v^2)=1$

Integrating, $v^2 = t + C$

Since the body starts from rest, at $t=0$, $v=0$, so $C=0$. Hence, $v^2=t \quad \Rightarrow \quad v=\sqrt{t}$

Find displacement

Velocity is $v = \frac{dx}{dt} = \sqrt{t}$

Therefore, $dx = \sqrt{t}\,dt$

Integrating from $0$ to $9$ s, $x = \int_0^9 \sqrt{t}\,dt$

$x = \int_0^9 t^{1/2} dt = \left[\frac{2}{3}t^{3/2}\right]_0^9$

$x = \frac{2}{3}(9)^{3/2}$

Now, $9^{3/2}=(\sqrt{9})^3=3^3=27$

So, $x = \frac{2}{3}\times 27 = 18\,\text{m}$

Final answer $\boxed{18}$

Comparison with stored correct answer

Stored correct answer = $18$

This matches the derived answer.