The position of an object moving along a line is given by the function $s(t)$, where $s$ is measured in feet and $t$ in seconds. We determine that the velocity is $v(t) = 4t + 1$ feet per second.

How much does the position change over the time interval $[0,4]$?
Change in position = feet

Suppose you are told that the object's initial position $s(0) = 7$. Determine $s(2)$, the object's position $2$ seconds later.
$s(2) =$

If you are told instead that the object's initial position is $s(0) = 3$, what is $s(2)$?
$s(2) =$

If we only know the velocity $v(t)=4t+1$ (but not the initial position), which of the following could be the position function?
Select all that apply.

A. $s(t) = 2t^2 + t +11$

B. $s(t) = 2t^2 + t$

C. $s(t) = 2t^2 + t +5$

D. $s(t) = 2t^2 + t + 20$

E. $s(t) = 2t^2 + t + 37$

F. None of the above

If, in addition to knowing the velocity function is $v(t) = 4t+1$, we know the initial position $s(0)$, how many possibilities are there for $s(t)$?

A. Infinitely many
B. 2
C. 1
D. 0
E. 5
F. none of the above