Question

At 2:00pm a car's speedometer reads 60mph, and at 2:10pm it reads 80mph. Use the Mean Value Theorem to find an acceleration che car must achieve Answer in mi/h):

Answer 1

120 mph²

Explanation:

The Mean Value Theorem states that there exists a time between 2:00pm and 2:10pm where the car's instantaneous acceleration matches its average acceleration over that time interval. To find the average acceleration, you can use the formula:

Average acceleration = (Change in velocity) / (Change in time)

Change in velocity = 80 mph - 60 mph = 20 mph

Change in time = 10 minutes = 10/60 hours = 1/6 hours

Average acceleration = (20 mph) / (1/6 hours) = 120 mph^2

This means that there must be a moment between 2:00pm and 2:10pm where the car's acceleration reaches 120 mph^2.