Question

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solve all problems algebraically unless you are specially asked to graph. you may always use graphing to check your answers.
if you are told to solve a specific way, you must do that to earn the points.
give all answers as exact answers unless you are asked to round.
notes: module 1 (answer key)
notes: module 2 (answer key)
notes: module 3 (answer key)
given that (s(t)=12t - t^{2}) is a position function where (s(t)) is measured in millimeters and (t) is time in seconds, find the average velocity (average rate of change) for (s(t)) between (t = 1) and (t = 3) seconds.
select an answer
*algebraic work must be shown to retain points on quizzes, midterm or final
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Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = s(t)$ over the interval $[a,b]$ is given by $\frac{s(b)-s(a)}{b - a}$. Here, $a = 1$, $b = 3$, and $s(t)=12t - t^{2}$.

Step2: Calculate $s(1)$ and $s(3)$

For $t = 1$, $s(1)=12\times1-1^{2}=12 - 1=11$ (mm).
For $t = 3$, $s(3)=12\times3-3^{2}=36 - 9 = 27$ (mm).

Step3: Calculate the average rate of change

The average rate of change $\frac{s(3)-s(1)}{3 - 1}=\frac{27 - 11}{2}=\frac{16}{2}=8$ (mm/s).

Answer:

8 mm/s