At 2:00 p.m. a car's speedometer reads 30 mi/h. At 2:10 p.m. it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the

Question

At 2:00 p.m. a car's speedometer reads 30 mi/h. At 2:10 p.m. it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h².
Let v(t) be the velocity of the car t hours after 2:00 p.m. Then [v(1/6) - v(0)] / (1/6 - 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 p.m. is exactly 120 mi/h².

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