exaniple 3 video example car over time interval tz t is the same as the average of its velocitie

1. We are given a function s(t) that represents the displacement of a car at time t.

Question

Example 3 Video Example Show that the average velocity of a car over a time interval [t1, t2] is the same as the average of its velocities during the trip. Solution If s(t) is the displacement of the car at time t, then, by definition, the average velocity of the car over the interval is (s(t2) - s(t1)) / (t2 - t1) On the other hand, the average velocity function on the interval is (1/(t2 - t1)) int_{t1}^{t2} v(t) dt = (1/(t2 - t1)) int_{t1}^{t2} s'(t) dt = (1/(t2 - t1)) [s(t2) - s(t1)] [by the net change theorem] 2. Find the average value f_ave of the function f on the given interval. f(x) = 322 [-1, 3] 3. Find the average value g_ave of the function g on the given interval. g(x) = cos(x), [7, 3]

          Example 3
Video Example
Show that the average velocity of a car over a time interval [t1, t2] is the same as the average of its velocities during the trip.

Solution
If s(t) is the displacement of the car at time t, then, by definition, the average velocity of the car over the interval is


(s(t2) - s(t1)) / (t2 - t1)

On the other hand, the average velocity function on the interval is

(1/(t2 - t1)) int_{t1}^{t2} v(t) dt = (1/(t2 - t1)) int_{t1}^{t2} s'(t) dt

= (1/(t2 - t1)) [s(t2) - s(t1)]  [by the net change theorem]

2.
Find the average value f_ave of the function f on the given interval.

f(x) = 322   [-1, 3]

3.
Find the average value g_ave of the function g on the given interval.

g(x) = cos(x),  [7, 3]

exaniple 3 video example car over time interval tz t is the same as the average of its velocities during the brip show that the average velocty of sohtion the at time then by definition the 79703

Added by Christopher P.

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