AP Calculus AB · Unit 8 · Applications of Integration

After a concert, a visitor walks along a straight walkway from a stadium gate. For $0 \le t \le 9$ minutes, the visitor's velocity is $v(t) = t^2 - 12t + 27$ meters per minute, where positive velocity means moving away from the gate. At $t = 0$ the visitor is at the gate.

(a) Find the acceleration of the visitor at $t = 5$. Is the visitor's speed increasing or decreasing at $t = 5$? Give a reason for your answer.
(b) Find the visitor's greatest distance from the gate for $0 \le t \le 9$. Justify your answer.
(c) Find the average value of this visitor's speed on the interval $0 \le t \le 9$.
(d) Find the average velocity of the visitor over the interval $0 \le t \le 9$.