Preview Activity 1.1.1.
Suppose that the height \(s\) of a ball at time \(t\) (in seconds) is given in feet by the formula \(s(t) = 64 - 16(t-1)^2\text{.}\)
(a)
Construct a graph of \(y = s(t)\) on the time interval \(0 \le t \le 3\text{.}\) Label at least six distinct points on the graph, including the three points showing when the ball was released, when the ball reaches its highest point, and when the ball lands.
(b)
Describe the behavior of the ball on the time interval \(0 \lt t \lt 1\) and on time interval \(1 \lt t \lt 3\text{.}\) What occurs at the instant \(t = 1\text{?}\)
(c)
Consider the expression
\begin{equation*}
AV_{[0.5,1]} = \frac{s(1) - s(0.5)}{1-0.5}\text{.}
\end{equation*}
Compute the value of \(AV_{[0.5,1]}\text{.}\) What does this value measure on the graph? What does this value tell us about the motion of the ball? In particular, what are the units on \(AV_{[0.5,1]}\text{?}\)
