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coldgirl
3 days ago
7

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 acce

leration is exactly 120 mi/h2. Let v(t) be the velocity of the car t hours after 2:00 PM. 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 PM is exactly 120 mi/h2.
Mathematics
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