Physics Saves the Day (or Ruins It, Depending on Your Perspective)

Here's a very brief synopsis of the mock trial fact situation. Illegal street racing is popular in this town. There is a minor rivalry between two college students over this activity. A bunch of students, including these two go "caravanning" to this fast food restaurant. They stop at a light, one of the rivals drives up beside the other, and shouts that she wants to race. The light turns green, they both accelerate, the taunting student looses control of the car, crashes, and subsequently dies. The other car allegedly accelerates and then decelerates abruptly as the driver sees the crash. The student who doesn't crash--the one being taunted--is charged with second-degree manslaughter, or in the alternative, criminally negligent homicide. If this seems absurd, it's because I left out a few facts to simplify the description. There is an interesting testimony by an "expert" witness who gives his analysis of the situation by stating key speeds, times, distances, and accelerations. You can probably tell where this is going.

I read this testimony last night, and was utterly confused. It was clearly written by someone with absolutely no clue about physics whatsoever. My favorite passage is:

Parker Gallo's statement that Dana's vehicle crossed the intersection quickly would be consistent with a vehicle that is accelerating at a maximum velocity. We measure that velocity from zero to sixty miles per hour.

Moderately humorous, eh? But it gets better.

We were sitting at practice analyzing the case, when Kim Pelster made some idiotic comment about how I should study the physics of the situation, making a really annoying jab at my interest in the subject, and surely trying to embarrass me in front of Judge Giles. Tonight I was reading over it all again and thought about it. While the thought of Kim being potentially right really bugged me, I decided to crunch the numbers anyway--for the sake of the team.

Based on the incompetent information in the testimony, one can calculate two completely conflicting estimates for the cars velocity. The car's top acceleration is 0-60mph in 7s, which equals about 12.6ft/s². Using the two conflicting velocities, some the expert's other estimates, and my favorite of Zaraza's "sacred laws of motion" (v_f² + v₀² = 2aΔx) one can calculate that the car was either accelerating at about 5.9 ft/s or would have had to have travelled about 50% farther than it actually did. We can toss out the second conclusion as bogus. This means that the car would have had to have accelerated at less than half of its maximum, indicating that the driver was clearly not trying to race. It also suggests that this witness for the prosecution is completely incompetant, also furthering the case of the defense.

The only potentially serious assumption that I believe I'm making is that of constant acceleration. I think it is reasonable, though, because the car only travels a total of 135 feet before stopping. Since there was a quarter mile before the next stop in traffic, I think it makes sense to assume that a rational driver would accelerate fairly constantly under these circumstances, whether racing or driving normally. The driver would want to get up to full speed, which would probably take more than a hundred feet in either situation. Furthermore, witnesses on both sides agree that the car's accelerator pedal became stuck. We know that it was depressed in some degree the whole time, at least until the moment of braking.

I guess it's okay for Kim Pelster to have a good idea just this once. The irony is worth it.