Mean Value Theorem and the police A sune patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another patrol officer 30 mi along the highway. When the car reached the location of the second officer 28min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the 60-mi/hr speed limit. Why can the officer conclude that the driver exceeded the speed limit ?

Solution 29E Step 1 We are given that, a first patrol officer saw a car start from rest at a highway. She radioed ahead to another patrol officer 30 mi along the highway. When the car reached the location of the second officer 28min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the 60-mi/hr speed limit. We have to find why the officer conclude that the driver exceeded the speed limit. Step 2 Consider the place of first patrol officer to be f(a) = 0 mi Let the place of second patrol officer to be f(b) = 30 mi 0 Consider the time to be a = 0 min = 60hrat f(a) = 0 mi 28 And the time to be b = 28 min = 60 hrat f(b) = 30 mi The pictorial representation of the problem is shown below