# Mean value theorem

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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#### Solution Preview

Proof:

Since the acceleration a is the derivative of the speed v, in other words, a=dv/dt.

Suppose v=f(t), the speed v is a function of ...

#### Solution Summary

This uses the mean value theorem for the speed of a car.

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