A plane begins its takeoff at 2:00 P.M. on a 2200-mile flight. After 12.5 hours, the plane arrives at its destination. Explain w
hy there are at least two times during the flight when the speed of the plane is 100 miles per hour.A) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 303 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 303 mi/hr and decelerating from 303 mi/hr.B) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 152 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 152 mi/hr and decelerating from 152 mi/hr.C) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 88 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 88 mi/hr and decelerating from 88 mi/hr.D) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 117 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 117 mi/hr and decelerating from 117 mi/hr.E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 176 mi/hr and decelerating from 176 mi/hr.
E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 176 mi/hr and decelerating from 176 mi/hr.
Step-by-step explanation:
In this question we have the average velocity v = 2200/12.5
= 176miles/hr
The function Which describes the velocity of a plane is continuous. At point t, f(t) is equal to 176. So by the mean value theorem we arrive at a conclusion that the velocity is going to attain the speed of 100 miles per hour twice. The first time is during acceleration, and the second time is during deceleration. So by this, the answer to this question is option E.
