If the speed limit is 60 mph, can the police cite you for speeding.

Question

At 10:17 am you pass a police car at 55 mph that is stopped on the freeway. You pass a second police car at 55 mph at 10:53 am, which is located 39 miles from the first police car. If the speed limit is 60 mph, can the police cite you for speeding.

(they probably won't, but can they mathematically?)

Answer 1

Let f(t) = distance travelled t hours after passing the first police car

f(0) = 0 and f(0.6) = 39

f'(t) = speed at time t

Assuming that the conditions of the Mean Value Theorem are met, there is at least one time, c, between time 0 and time 0.6 hours such that:

f'(c) = (f(0.6) - f(0)) / ((0.6 - 0) = 39 / 0.6 = 65 mph. Yes, the driver was speeding sometime during the timeframe in question. Hopefully, the state troopers did not take Calculus.

Answer 2

d / t = r

39 / (36/60) = ?