At 2:00 PM a car\'s speedometer reads 30 mi/h. At 2:10 PM it reads 50 mi/h. Show

Question

At 2:00 PM a car's speedometer reads 30 mi/h. At 2:10 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h2.

At 2:00 PM a car's speedometer reads 30 mi/h. At 2:10 PM 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) be the velocity of the car t hours after 2:00 PM. Then 1/6) Let v(t) be the velocity of the car t hours after 2:00 PM. Then By the Mean Value Theorem, there is a number c such that with 1/6-0 v'(c) = Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 120 mi/h2

Explanation / Answer

I am assuming the speed function to be continuous and differentiable and then I will be using Mean Value Theorem

(v(b)-v(a)) / (b-a)
= (50 - 30)/(1/6)
= 20*6
= 120 mi/h^2

By the mean value theorem, there is a number c such that 0<c<1/6 where
v'(c) = 120 mi/h^2.

Hence proved that at some time c acceleration will be 120 mi/h^2

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