Beginning at the same time and location, Athletes 1 and 2 run for 30 seconds along a straight track with velocities v 1 (t) and v 2 (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 a...

a The area of the shaded region over 0 10 represents how much further Athlete 1 ran than Athlete 2 o ...

Beginning at the same time and location, Athletes 1 and 2 run for 30 seconds along a

Question:

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.

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

(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?

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