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How To Calculate Speed at moment of Impact

  1. Nov 21, 2011 #1
    First of all, let me apologize for being a total math newb. I love geometry but I barely made it out of algebra alive...and that was 21 years ago.

    My girlfriend was recently involved in a car accident where she was charged with "Failure To Yield". Based on a spectacularly non-stellar, non-investigation by our local police department I have taken it upon myself to attempt to calculate the speed of the vehicle that stuck her (car) based upon the distance her car was moved during the accident. I'm aware that there are numerous variables that some of you are likely to want and I will do my best to supply them as requested/demanded. I'm unsure as to whether this is a problem to be solved with a velocity equation or a true speed equation with which I'm unaware.

    Vehicle A is a 2000 Volvo V70 station wagon. Weight is approximately 4,690 pounds. 5 gallons of unleaded fuel onboard at the time at 6.4lbs/gal = approx 32lbs. Driver weight is 115lbs. 150 lbs of horse feed was also onboard at the time. Total weight approx 4,987 lbs at the time of collision.

    Vehicle B is a 2000 Mitsubishi Gallant with 02 POB. Person 1 = approx 220 lbs; Person 2 = approx 120 lbs. Vehicle wt approx 3,270 lbs. Fuel/baggage unknown. Approx Wt subtotal with fuel unkown is 3,610 lbs.

    B impacted A slightly forward of the driver's door causing significant impact damage but very little rotational spin. Straight-line distance moved was approximately 48 feet before Vehicle A rotated approximately 35 degrees clockwise and came to a halt and Vehicle B rotated approximately 15 degrees counter-clockwise and travelled an additional 29 feet.

    How would I (you?) go about calculating speed of Vehicle B at time of impact. Speed of Vehicle B was less than 5mph at time of broadside collision (pulling out of a parking lot).

    There are numerous theories regarding why Vehicle B never applied the brakes before striking Vehicle A, but for now I'm attempting to stick with facts rather than hyperbole. I'm working on creating some diagrams to present to several people and if they would be helpful I can attempt to scan them in and upload them with this question.

    Again, thank you for any direction you may be able to provide.
  2. jcsd
  3. Nov 21, 2011 #2
    I am not sure how accurate this is as I had to really simplify things:

    Mass A is 2259 kg(volvo)
    Mass B is 1637.5kg(mitsubishi)

    The coeffecient of friction for asphalt and rubber is between .5-.8, the displacement of mass A is 14.6m, For Mass A the normal force is 22138N, so the work required to overcome friction for 14.6m is 161.6-258.6 kJ

    KE = .5mv2 using this I get that the car must have been accelerated to a velocity of between 11.9 - 15.1 m/s

    That would be a momentum of between 26882 - 34181.2 kg*m/s

    dividing these by Mass B gives between 16.4 - 20.9 m/s (37-47mph)

    Don't take my word for it but I think all the simplifications lead to a greater impact when corrected, such as the absorbed energy, the rotational energy put into both. There is my guess anyway
  4. Nov 23, 2011 #3
    Wow! I'd briefly thought about friction of rubber on asphalt, but "thinking about" it was as far as I'd gotten! This isn't what I expected at all but it's VERY interesting nonetheless.
  5. Nov 23, 2011 #4


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    If you really want to use the marks on the road as good evidence then you would need to do what professional crime and accident investigator have to do. They look at the details of many other documented collisions where the speeds and vehicle masses were known and compare the marks with the ones in this case. It's more an exercise in statistics than a precise dynamics calculation, I think. This info may be available.

    There are tables of speed vs braking distance (Driving test knowledge) or speed vs skid distance, which could give an indication of the speeds of both cars immediately after impact, by extension (Tyres must have a similar behaviour whichever way they are sliding across the road). Then a simple Conservation of Momentum calculation could suggest a speed for the colliding vehicle. I'm assuming that Car A was not moving significantly before the impact and that any rotation is not significant.

    It would be very possible to come up with some ball-park figures (from some of the above ideas) but I would suggest that an opposing lawyer would soon knock holes in them as evidence unless you could come up with a lowest possible speed for the approaching driver that was way above the legal limit..
  6. Jul 3, 2012 #5
    I too, was involved in a car accident this morning. I got a ticket for failure to yield. Similar to other story. I was driving a 2006 Volvo XC 70 Wagon, she had a 95 Honda Accord or something lik that. She was the sole passenger, 100-120lbs, and I was in with my daughter, 180lbs, and 85 lbs. I turned left, and she hit me in the rear quarter of the vehicle spinning me around, and she kept going on straight through with blown out front tire for an additional 45.10 feet.

    She was definitely speeding. I calculated the after impact speed according to the skid after hit of 45.10 feet to be approx. 33-35 mph.

    What could have been the pre-collission speed.
  7. Jul 3, 2012 #6
    Clarification on the rear quarter for exactness:

    The hit to my Volvo was the back side of the rear passenger door to rear tire area.
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