Graphical representation:
Here, OC is the total displacement.
Resolving vector OA into its components.
[tex]OA=70\cos (60\degree)\hat{i}+70\sin (60\degree)\hat{j}\ldots(1)[/tex]Resolving vector AB into its components.
[tex]AB=100\hat{i}\ldots(2)[/tex]Resolving vector BC into its components.
[tex]BC=-80\cos (45\degree)\hat{i}+80\sin (45\degree)\hat{j}\ldots(3)[/tex]The resultant vector OC is given by the adding equations (1), (2), and (3),
[tex]\begin{gathered} OC=\lbrack70\cos (60\degree)+100-80\cos (45\degree)\rbrack\hat{i}+\lbrack70\sin (60\degree)+80\sin (45\degree)\rbrack\hat{j} \\ =78.43\hat{i}+117.19\hat{j} \end{gathered}[/tex]The magnitude of the displacement vector OC is given as,
[tex]\begin{gathered} \lvert OC\rvert=\sqrt[]{(78.43)^2+(117.19)^2} \\ \approx141\text{ m} \end{gathered}[/tex]The average velocity is given as,
[tex]\begin{gathered} v_{av}=\frac{\text{ total displacement}}{\text{total time taken}} \\ =\frac{\lvert OC\rvert}{t_1+t_2+t_3} \end{gathered}[/tex]Substituting all known values,
[tex]\begin{gathered} v_{av}=\frac{141\text{ m}}{15\text{ s}+20\text{ s}+10\text{ s}} \\ \approx3.13\text{ m/s} \end{gathered}[/tex]Therefore, the average velocity is 3.13 m/s.
