Let me comment only on your computations. As for what you and the officer argue about, I am out---because you did not mention what was it exactly, what his report was, how would distance computations combat speeding problems,....
Yes, if the acceleration is 10 ft/sec/sec, then a car from rest will cover 125 ft in 5 seconds:
d = (Vo)t +(1/2)*a*t*t
d = (0)(5) +(1/2)*10*5*5
d = 125 ft.