Preview Activity 4.1.1.
Suppose that a person is taking a walk along a long straight path and walks at a constant rate of 3 miles per hour.
(a)
On the left-hand axes provided in the following figure, sketch a labeled graph of the velocity function \(v(t) = 3\text{.}\) Note that while the scale on the two sets of axes is the same, the units on the right-hand axes differ from those on the left. The right-hand axes will be used in question (d).
(b)
How far did the person travel during the two hours? How is this distance related to the area of a certain region under the graph of \(y = v(t)\text{?}\)
(c)
Find an algebraic formula, \(s(t)\text{,}\) for the position of the person at time \(t\text{,}\) assuming that \(s(0) = 0\text{.}\) Explain your thinking.
(d)
On the right-hand axes provided in the provided figure, sketch a labeled graph of the position function \(y = s(t)\text{.}\)
(e)
For what values of \(t\) is the position function \(s\) increasing? Explain why this is the case using relevant information about the velocity function \(v\text{.}\)
