Problem

Topic -Mean Value Theorem

You are driving on a freeway. At 10:20 am, driving at a speed of 55 mph, you pass a parked police car. At 10:56 am, driving at a speed of 55 mph, you pass another parked police car. The second police car is parked 39 miles from the first one. Assume both highway police officers communicate with each other. As the speed limit on that freeway is 60 mph, the second police officer gave you a speeding ticket. Justify the police officer's action.

Hint: In a motion along straight line, s(t) is the distance travelled, v(t)=s(t) is the velocity (speed with direction).

Part A: Using information in the problem, draw a reasonable graph (exact unknown), taking time t along X-axis and distance along the Y-axis. Let the time 10:20 am be t=0 at which distance s=0. Graph must show the starting point (first police car) and the ending point (second police car). Graph must visually indicate the starting and ending speeds of 55 mph being same. It is enough if the X and Y axis are labelled only for starting and ending points. Upload distance graph.

Part B: Why is the police officer justified in giving you a speeding ticket? How can the officer be sure that you drove above speed limit? Upload paperwork.