Using physics in accident investigation

[physicsbum]

i have an assignment in physics due tomorrow and i would really appreciate it if someone could explain to me how acceleration, velocity and displacement are used to investigate accidets. Or if you know of any great sites i could go on to find this information would be very helpful.

please respond soon i really need help..

thanks.. physicsbum

 

[brewnog]

Homework assignment eh?

How about you let us know some of the ideas you had.

 

[physicsbum]

ughh.. ideas?? my topic is how physics is used to recreate traffic accident like car crashes... soo far ill i know is that by determining the distance of a skid mark and the coefitiant of friction i can figure out how fast the car was going... but i still don't know how to find acceleration or displacement...

 

[denverdoc]

Physicsbum, do you know any of the kinematic equations that might apply?

aslo can you explain mathematically what you mean above about skid marks, etc?

 

[physicsbum]

im not entierly sure but i think to determine velocity i have to use the formula
V=squreroot of fd...
but if i knew i was right, i wouldn't exactly be asking for help now would i?

 

[denverdoc]

well it's important to know what knowledge you do have if we are to be most helpful. Let's just consider the skidmark. In the case of most accidents I think it can be assumed to be a panic stop where one slams on the brakes and has no ABS. The first piece of evidence maybe helpful to such an investigation is where it starts in relation to the accident. If it is a few feet away from a collision where a stalled car is struck by moving vehicle, we can assume either one of two things, the driver was either inattentive or traveling at high speed or both. The amt of damage to the cars is a clue to help decide which is it. That the stalled car might have been sent 100 or more feet would be of help as well for reasons of momentum conservation.

From the length of such a skidmark we might also be able to infer the speed at which the car was traveling when it struck the other vehicle, as well as when the brakes were applied in conjunction with other evidence, as you decided correctly, tho the exact eqn is a bit different. Do you want more help with math or with general principles?

 

[physicsbum]

ohhhh man you are a life saver!
please help me a little with the math first and maybe later we can get into general principles!

 

[physicsbum]

could you please show me what the exact equation looks like?

 

[denverdoc]

first a warning, these equations apply for constant acceleration/deceleration, which may or may not be valid in all circumstances.

Lets consider a case where we deduce from physical evidence that the collision (again hitting a stalled car, tho the same reasoning can be expanded to include other situations) occurred at 20mph. The skidmark is 50 feet long.

How fast was the driver moving when he hit the brakes?

We also know from lookup tables such as those that car magazines publish, that the car in question can stop optimally from 60MPH in 140ft.

If we convert mph into fps (feet per second) that's 90fps.

There is an eqn that is Vf^2-Vi^2=2*ad where a is the acceleration and d the distance required to stop. Since the final velocity is zero,
we can compute a, that is the maximal deceleration the cars brakes can provide.

Using this a, we can then determine how fast the car was moving when the driver hit the brakes, using the same eqn, uinder the assumption of 20mph collision.

 

[physicsbum]

ok yea I've done this before and i recognize the formula.. soo i guess my other formula v=Sqreroot of 2*f*d was totally wrong.. ohwell

... so to find displacement and acceleration how would i re arrange the formula?? and could you also give examples like the previous on please and thank you...

 

[denverdoc]

well we could be at this all night, and the idea is to help, not just to provide answers,

But your formula was not all wrong by any stretch, just comes at the problem from another angle that involves energy, instead of force.

Lets see what you can make of the following: this is a head on collision:
luckily both drivers survived, but there is a legal battle now between insurance companies.

Driver a is in a Porche Carrera behind a truck and attempts to pass, but before he gets back into his own lane, strikes an oncoming rust bucket. He swears under oath, that he had plenty of distance between the rust bucket to make the maneuver safely but that the rust bucket deliberately sped up so as to cause a collision. There are two sets of skidmarks, one short made by the Porsche, and a much longer one made by the rust bucket. Who do you believe and why?

 

[physicsbum]

i would believe the rust bucket because the skid marks were longer.. I am not exactly sure..
but for my assignment i don't really have to know general principles.. i just need to explain how to find displacement or acceleration and relate it to a car accident

 

[denverdoc]

right if the porsche drivers claim is true, then the rust bucket actually had a helluva lot horsepower to lay tracks for a longer distance than did the Porsche (who arguably had better tires.) Luckily physics can help us here as well as the 1/4 mile times and 0-60stats could prove whether the car was accelerating or decellerating, (likely forensic evidence of looking at the patch of rubber could help too).

Well the eqn I have given is the right one:

in general X=Xo+Vo(t)+1/2 at^2. Vf=Vi+at, and the one i posted above are the most salient. These can be rearranged many ways. There are so many excellent sources on line re kinematics, I would invite you to explore the subject further.

 

[physicsbum]

ok.. how would displacement be used to investigate accidents??

 

[denverdoc]

Displacement is just a fancy term for distance, right. Let's take the example of a car that drives off the cliff and attempt to determine whether it was suicide or sleepiness. We know that the average reaction time between perceiving a threat and responding is 0.4 seconds. Displacement is defined as above, X. If there is no acceleration, just velocity times time. So how could you decide between a suicidal driver intent on deceiving insurance company and a genuine case of sleeping at the wheel. Take direction into account, where did the car end up?