At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h2.

Question

Let v(t)

 be the velocity of the car t hours after 2:00 PM. Then v(1/4) - v(0)/1/4 - 0 = ???

By the Mean Value Theorem, there is a number c such that 0 < c < ??? with v'(c) = ??? . since v'(t)

 is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 80 mi/h².

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Answer 1

What is the average accelerations convert (50-30)/ 0.25 (15 minutes is 0.25 hours)

average acceleration is 80. The mean value theorem says a derivative of a smooth function must take on the average rate of change between two points. on the interval between those points.