A particle of mass $1 kg$ is moving along $X-$axis. Its velocity is $6 m/s$ at $x=0$. Acceleration-displacement curve and potential energy-displacement curve of the particle are shown:

Area of $\left(a-t\right)$ curve $=32 m{s}^{-1}=V_f-V_i$

$V_f=32+V_i=32+6=38 m{s}^{-1}$

work done by all forces $=∆KE$

$=\frac{1}{2}m\left(V_f^2-V_i^2\right)=\frac{1}{2}\left({38}^2-6^2\right)=704 J$

work done by conservation forces

$U_i-U_f=320 J$

work done by external forces $=704-320=384 J$