Answer
The displacement vector for the olive and nut are $57.689\vec{r}$ and $19.229\vec{r}$ respectively, where $\vec{r}$ is the unit vector for displacement.
Work Step by Step
By Newton's 2nd law, $\vec{a_o}=(\frac{2}{0.5},\frac{3}{0.5})=(4,6)$ and $\vec{a_n}=(\frac{-3}{1.5},\frac{-2}{1.5})=(-2,-\frac{4}{3})$.
Using the kinematic equations, the final position would be, $x_f=x_0+\frac{1}{2}\vec{a}t^2$.
For the olive, $x_f= (0,0)+ \frac{1}{2}(4,6)(4)^2=(32,48)$. The total displacement would be, $\sqrt{32^2+48^2}=57.689$m
For the nut, $x_f= (1,2)+\frac{1}{2}(-2,-\frac{4}{3})(4)^2=(-15, -\frac{26}{3})$. The total displacement would be $\sqrt{(-15-1)^2+(-\frac{26}{3}-2)^2}=19.229$m
