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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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.

This problem is about the proof of Theorem 1 implies Theorem 2 as discussed in class. Regard Theorem 1 as a statement P and Theorem 2 as the statement "Q implies R". Then the statement "Theorem 1 implies Theorem 2" can be expressed as:
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Theorem 2" is can be expressed as P implies (Q implies H)".
a

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