Chapter 3.4, Problem 33E

$\boxed{\text{T}}$ Exercise 31-34 give the position function $s=f\left(t\right)$ of an object moving along the $s$-axis as a function of time $t$. Graph $f$ together with the velocity function $v\left(t\right)=ds/dt=f^{\prime }\left(t\right)$ and the acceleration function $a\left(t\right)=d^{2}s/d{t}^2=f^{″}\left(t\right)$. Comment on the object’s behavior in relation to the signs and values of $v$ and $a$. Include in your commentary such topics as the following:

1. When is the object momentarily at rest?

2. When does it move to the left (down) or to the right (up)?

3. When does it change direction?

4. When does it speed up and slow down?

5. When is it moving fastest (highest speed)? Slowest?

6. When is it farthest from the axis origin?

$s=200t-16t^2,\text{ 0}\le \text{t}\le \text{12}\text{.5}$(a heavy object fired straight up from Earth’s surface at $200\text{ft/sec}$)