5. The radar guns that police ofcers use re a radio wave which bounces off an object and returns to the gun. The gun measures the amount of time it took for the wave to return, and from this time it determines the vehicle's position, 5 (1). With a second measurement, the gun can determine the object's velocity, v (t). (a) What is the relationship between an object's position, 3 (t), and its velocity, v (t)? Hint: You can email me if you don't know. We haven't really talked about it in class. (b) Explain why the Mean Value Theorem applies to an object's position function. Him: I am not looking for a profound disquisition on Physics. A few words will do. (-2) Suppose a radar gun determines that a car's positions at times t = 0 sec andt = lsec are .5 (0) = 250 ft and s (1) = 150 ft, respectively. Use the Mean Value Theorem to show that at some point over that interval, the car was traveling faster than 100 mph. Hint: You'll need to convert units