# Using the mean value theorem to prove the acceleration at a specific moment in time.

At 2:00 pm a car's speedometer reads 30 mi/h. At 2:10 pm it reads 50 mi/h. Use the mean value theorem to show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h^2. Please show line by line work and be as clear as possible.

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...the time t.

At time t1=2:00pm, v1=f(t1)=30mi/h.

At time t2=2:00pm, v2=f(t2)=50mi/h.

Since f is a differentiable function, by the ...