For an airplane to take-off it accelerates according to the graph shown and takes 12 s to take -off from the rest position. The distance travelled by the airplane in 6sec is

From 0 to A we have acceleration varying linearly with time 

Hence slope $=\frac{\mathrm{a}-0}{\mathrm{t}-0};\frac{5}{6}=\frac{\mathrm{a}}{\mathrm{t}}\frac{\mathrm{dv}}{\mathrm{dt}}=\frac{5}{6}\mathrm{t}$
$\begin{array}{l}{\int }_0^{{\mathrm{v}}_1} \mathrm{dv}=\frac{5}{6}{\int }_0^{\mathrm{t}} \mathrm{tdt}\\ {\mathrm{v}}_1=\frac{5}{12}{\mathrm{t}}^2;{\mathrm{V}}_1=\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{5}{12}{\mathrm{t}}^2\\ {\int }_0^{{\mathrm{x}}_1} \mathrm{dx}=\frac{5}{12}{\int }_0^6 {\mathrm{t}}^2\mathrm{dt}=\frac{5}{36}{\left({\mathrm{t}}^3\right)}_0^6=\frac{5}{36}\times 6^3\end{array}$

x₁ = 30m