Chapter 14.3, Problem 2QC

Find the functions that give the speed of the two objects in Example 2, for t ≥ 0 (Corresponding to the graphs in Figure 14.15).

Example 2 Comparing trajectories

Consider the trajectories described by the position functions

$r(t)-\langle t,t^2-4,\frac{t^3}{4}-8\rangle$, for t ≥ 0, and

$R(t)-\langle t^2,t^4-4,\frac{t^6}{4}-8\rangle$, for t ≥ 0,

Where t is measured in the same time units for both functions.

a. Graph and compare the trajectories using a graphing utility.

b. Find the velocity vectors associated with the position functions.

Figure 14.15