How can I prove my innocence in a three-car crash using physics?

[middleCar]

I need to do some homework for court. It has been more than 30 years since I was in a physics class.

I was the middle car in a three-car crash at a stop light - traffice started to move after the light turned green, then all of a sudden someone in the line in front hit their breaks. The vehicle in front of me stopped. I stopped. Then I was hit from behind.
I can find out the weights of all the vehicles involved and the approximate distance my vehicle traveled after inpact (12-14 feet) from the rear until it hit the vehicle in front of me and the distance that vehicle traveled (2-3 feet) after impact.

What I need to find out is: how fast was the vehicle that hit me going and how much distance I should have been from the vehicle in front of me to avoid hitting it. I don't believe that I can simply add 12 and 2 or 14 and 3 to get the answer because I asssume that my vehicle and the vehicle I hit must have absorbed some of the energy generated by the vehicle that hit me ... as did that vehicle.

The vehicle that hit me had to be towed because the front end was demolished and my vehicle is badly damaged: there is a crease in the driver's side rear quarter panel, the tailgate is inoperable, the sliding side door is jamed and will not open, the rear fender is destroyed, the front fender is cracked. The vehicle I hit has minor damage -- the rear fender is scraped and slightly dented.

And I got cited for "following too close"! I say there is no way as 12-14 feet is just about a car length.

I need to try to work out the physics to prove it in court.

Thanks!

 

[brewnog]

There are a lot of factors here.

Cars will indeed absorb energy in a collision, and with other factors (handbrake being applied, footbrakes being applied, car being in gear) you're not going to get exact answers.

The distance you should have maintained from the car in front has nothing to do with any vehicles behind you, as you know. Along with road, tyre, driver and car conditions, the safe stopping distance is related to the speed you are travelling. If you were stationary (as a result of the car in front stopping) at the moment you were hit, and you didn't hit the car in front (until you'd been bumped up the arse), I would think you are unlikely to be given any share of the blame for any damage caused. However, words like "fender" hint to me that you're in a certain litigious country where who gets sued is anyone's guess. I hope nobody was injured.

When I was a learner, I suddenly stopped at some lights which were, in fact, green. The car behind smacked into my back bumper. Practically speaking, it was my fault, and my inexperience had caused an accident. Legally speaking, it was the guy behind's fault for not keeping enough of a distance behind me.

Finally, you might find the following stopping distance calculator handy.

http://www.csgnetwork.com/stopdistcalc.html

 

[Danger]

The distance you should have maintained from the car in front has nothing to do with any vehicles behind you, as you know. Along with road, tyre, driver and car conditions, the safe stopping distance is related to the speed you are travelling. If you were stationary (as a result of the car in front stopping) at the moment you were hit, and you didn't hit the car in front (until you'd been bumped up the arse), I would think you are unlikely to be given any share of the blame for any damage caused.

The law here (although no one seems to obey it) is that when traffic is stopped, you have to allow enough room behind the next car to steer past it if necessary. That depends a lot upon what reflex speed you have, but the general rule is that you should be able to see its rear tires where they contact the road. This doesn't help much in a situation like yours, because there's no way to predict how hard you might get hit from behind. Twelve to fourteen feet certainly sounds safe enough.
For insurance purposes only, every vehicle is considered to be responsible for damage to the one ahead of it, regardless of what caused the impact. This doesn't affect any legal aspects of the situation, and someone in your position would never be charged with anything or lose license points. Any resultant lawsuits would be directed at whoever caused the first impact, since all intermediaries are considered blameless.
By the way, why aren't the police accident scene investigators doing their job? The full reconstruction documentation should be available to you for use in court. Every factor, from vehicle speeds to type of braking equipment and road surface conditions, should already be accounted for. Get your lawyer to subpoena them if necessary. If such investigation has not been performed, you should get the case dismissed for lack of evidence.