Activity 1.1.3.
Each of the following questions concern \(s(t) = 64 - 16(t-1)^2\text{,}\) the position function from Preview Activity 1.1.1.
(a)
Compute the average velocity of the ball on the time interval \([1.5,2]\text{.}\) What is different between this value and the average velocity on the interval \([0,0.5]\text{?}\)
(b)
Use appropriate computing technology to estimate the instantaneous velocity of the ball at \(t = 1.5\text{.}\) Likewise, estimate the instantaneous velocity of the ball at \(t = 2\text{.}\) Which value is greater?
(c)
How is the sign of the instantaneous velocity of the ball related to its behavior at a given point in time? That is, what does positive instantaneous velocity tell you the ball is doing? Negative instantaneous velocity?
(d)
Without doing any computations, what do you expect to be the instantaneous velocity of the ball at \(t = 1\text{?}\) Why?
