Question

If an object moves in a straight line with position function s = f(t), then the average velocity between t = a and t = b is




f(b) - f(a)/b - a




And the velocity at t = c is f '(c). Thus the Mean Value Theorem tells us that at some time t = c between a and b the instantaneous velocity f '(c) is equal to the average velocity. For instance, if a car traveled 1600 km in 20 hours, then the speedometer must have read ?????? km/h at least once.



In general, the Mean Value Theorem can be interpreted as saying that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval

Answer 1

The speed of the automobile is 75 km/hr according to the Mean Value Theorem.

It may be said that the immediate rate of change and the average rate of growth across an interval are identical at some numbers according to the Mean Value Theorem.

Therefore, an automobile would go 150 kilometers in 2 hours.

Then;

f(t=0) = 0

f(t = 2 hours) = 150 km

Therefore;

The average speed between t = a & t = b for an object moving with a position function of s = f(t) equals f(b) - f(a)/b - a.

f'(c) (speedometer reading) = f(t=2)-f(t=0) ÷ (2-0)

f'(c) (speedometer reading) = 150 ÷ 2  km/hr

f'(c) (speedometer reading) = 75 km/hr

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