Consider the following position functions r and R for two objects.

a. Find the interval [c, d] over which the R trajectory is the same as the r trajectory over [a, b].

b. Find the velocity for both objects.

c. Graph the speed of the two objects over the intervals [a, b] and [c, d], respectively.

r(t) = (4 + t², 3 - 2t⁴, 1 + 3t⁶), [a, b] = [0, 6],

R(t) = (4 + ln t, 3 - 2 ln² t, 1 + 3 ln³ t) on [c, d]
For graphing, let c = 1 and d = 20.