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Speed and distance in a car crash

  1. May 28, 2012 #1
    I had a car accident and need to go to court to prove my case. Please help me figure this out with what formulas I need to use. Also please explain details so I can explain it to the judge. Thanks. Here it is: I was traveling when I hit a car that pulled out in front of me. She claims she was making a left turn and that I hit her vehicle on the corner hard enough to push her vehicle sideways. I need to know how fast I would need to be going to move the back of her vehicle sideways anything more than an 1".
    Here is the data:
    Weight of my vehicle: 3196 lbs
    Weight of her vehicle: 3009 lbs
    My speed before impact: 25 MPH
    Her speed before impact: o mph
    Payment: Asphalt
    Weather conditions: Dry 70 degree F
  2. jcsd
  3. May 28, 2012 #2

    Simon Bridge

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    Homework Helper

    Jones and Childers report coefficients of friction of about µ=0.7 for dry roads

    The force opposing motion would be µW=(M+W)a: W is the weight of her car and M is the weight of yours - a is the deceleration. the distance slid is given by d=v²/2a where v is the initial speed of both cars.

    Back of envelope, you'd use conservation of momentum to estimate the speed of both vehicles together after the collision but before lateral movement.

    Mu=(M+W)v where u is the speed of your car before the impact.

    Plugging in the numbers I get 27cm lateral movement: about a foot.
    There's an awful lot of assumptions in that but at least it does not look all that sensitive to even quite large changes in speed (I still get less than a foot for u=50mph).
    That's for pushing the whole car - for just the back you'd be rotating about the front wheels and only the weight on the back wheels will count for F. If I guess half (it will be less - engine is in the front right?) and just stay linear the guess turns into 72cm - a bit over two feet.

    However: my experience is that judges are seldom impressed by this sort of reasoning unless you get an expert witness to deliver it. What you really need is an expert in accidents or a practical experiment.
  4. May 28, 2012 #3


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    If she attempted a left turn from opposing traffic or from a side street while it was not safe to do so would mean that her manoeuvre was the probable cause of the accident.
    If you rear-ended her then most likely your inattention on the road that is the probable cause of the accident. Unless she changed lanes and braked in front of you and you hit her in which case the main party at fault is for a debate.
    Unless you can prove to the judge that you are an expert in some aspect of road collisions and damage ensued, I doubt that a momentum and energy calculation would impress the judge, as SB stated.
  5. May 28, 2012 #4
    Thanks for the help. Will keep that in mind about want impresses the judges.
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