Beginning at the same time and location, Athletes 1 and 2 run for 30 seconds along a straight track with velocities v₁(t) and v₂(t) (in meters per second) as shown in Figure 23.

(a) What is represented by the area of the shaded region over [0, 10]?
(b) Which of the following is represented by the area of the shaded region over [10, 30]?
i. How far Athlete 2 is ahead of Athlete 1 at t = 30.
ii. How much further Athlete 2 ran than Athlete 1 did over the last 20 seconds.
(c) Who is ahead at the end of each 5-second interval, t = 5, 10, . . . , 30?

(m/s) 7 6 5 4 3 2 1 5 2 10 15 20 25 +t(s) 30