At 9:13AM a car is traveling at 35 miles per hour. Two minutes later, the car istraveling at 85 miles per hour. Prove that are some time during this two-minuteinterval, the car’s acceleration is exactly 1500 miles per hour squared. Compute the value of A.

There is at least one instant which instantaneous acceleration is equal to average acceleration. .

Explanation:

The average acceleration experimented by the car is:

According to the Rolle's Theorem, there is at least one instant t so that instantaneous acceleration equal to average acceleration for the analyzed interval. That is to say:

If car is accelerating at constant rate, instantaneous acceleration coincides with average acceleration for all instant t. Then, instantaneous acceleration is:

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