First of all, Andy peeled out of there at about 0.82 of a 'G', and I'm sure
that he must have burned some rubber. So he may already be in some
trouble with the local gendarmerie.
But for the sake of answering the question, let's assume that nobody
heard it or saw it, and that Andy is free to go on his way after that
jackrabbit start. Also, lets assume that Andy's Wonder Machine can
keep up that kind of acceleration for 30 seconds, and that his stomach
stays with him all the way.
He gains speed at the rate of 8 m/s every second. So at the end of
30 seconds, he's moving at (30 x 8 m/s) = 240 m/s .
His average speed all the way, from zero at the beginning to 240 m/s
at the end, is (1/2) (0 + 240) = 120 m/s .
In 30 seconds, at an average speed of 120 m/s, provided he moves
in a straight line all the way, his displacement will be
(30 x 120) = 3,600 meters = 3.6 km
in whatever direction he's moving.
If he curves or skids anywhere along the way, then the displacement is
less than that.
Notice that Andy's speed at the end of 30 seconds ... 120 m/s ... is
about 537 miles per hour. So if the town cop decided to ignore
Andy's performance at the beginning of the 30 seconds, he is
definitely going to write Andy a speeding ticket at the end of it,
3.6 km from the light, as soon as he gets there.
