Physics Fought the Law, and Physics Won

Earlier today, I spotted this news article about a man who successfully disputed a speeding ticket given by an automated camera.  He superimposed the pair of timestamped pictures and showed that his speed could not have been the 50 mph that the ticket claimed.  The camera company countered that the speed is measured 50 feet before the photos are taken, so he may have slowed down.  This made me wonder exactly how fast he would have to be braking for such a theory to work.

Suppose he was going 50 mph when his speed was measured, then he braked to reach 35 mph (the speed limit) 50 feet later.  His acceleration is given by

Where vf and vi are the final and initial velocities, and t is the time spent decelerating.  Of course, we only know x, the distance he traveled, not t, so we have to find it using

Substituting into the original equation gives

or resolving for a,

Plugging in the values we have, the car would be decelerating at 15% the force of gravity.  According to Wikipedia, some roller coasters get up to 300% the force of gravity, so maybe the situation is more plausible than I first thought.  Whether the man was speeding or not, I commend him for using physics and the information available to him to make a convincing argument for his innocence.