The given position vector is
[tex]S(t)=\frac{t^3}{3}-\frac{15t^2}{2}+50t[/tex]
N0w the velocity will be
[tex]v(t)=t^2-15t+50[/tex]
Now,
[tex]\begin{gathered} v(t)\ge0,0\leq t\leq5,10\leq t\leq12 \\ v(t)<0,5So if the initial direction of the particle is towards the right, then in the interval 5
And if the initial direction of the particle is towards the left then the particle will move towards the right in the interval 5
