Question

Question attached as screenshot below, it's hard calculus please only accept if you are capable.

Answer 1

The given position vector is

`S(t)=(t^3)/(3)-(15t^2)/(2)+50t`

N0w the velocity will be

`v(t)=t^2-15t+50`

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