A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder at time t seconds is given by the parametric equations (7 +2t, 0). The location of the top of the ladder will be given by parametric equations (0, y(t)). The formula for y(t)=√[625−(7+2t)²]. The domain of t values for y(t) ranges from 0 to 9.
Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places):
a) [0,2]
b) [2,4]
c) [6,8]
d) [8,9]