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Physics of vehicle crash

  1. May 11, 2006 #1
    This is a real life situation, no homework associated. I am a mechanical engineer by degree, but have not actively worked in the field for over 20 years. However, I remember enough to be dangerous. I am looking for some high level, back of the envelope analysis. My wife was involved in an auto accident. She will be vehicle A.

    Vehicle A is heading south at a 4 way stop. Vehicle B is heading east (to the right of A). Vehicle A rolls to stop as 2 vehicles are crossing the intersection going east and west. Vehicle C is heading north, arrives at the intersection after both A and B. A is driving a mini van and B is driving a mid size car. Much discussion and confusion as to whether A or B arrived first, or both at the same time. The result is clear. Vehicle B impacts vehicle A and drives vehicle A into vehicle C. Vehicle A has $8k damage, vehicle B has deployed airbags, vehicle C is totalled. Yes, all from a 4 way stop. Vehicle B impacted vehicle A in an area centered about the rear wheel of vehicle A. Conditions were clear and sunny. Crash occured at 8 am on a Tuesday morning.

    Based on my memory of simple physics, the acceleration is distance divided by elapsed time squared. The velocity (average) is the distance travelled divided by the elapsed time. Force of impact is mass times acceleration.

    Since the time elapsed is not known, if I assume vehicles A and B start to enter the intersection at the same time, then the elapsed time between start of entry and crash will be the same for both vehicles. Thus, the relationship of the accelerations and average velocity is basically the ratio of the distance travelled. This is a typical semi-residential roadway in city limits. The lanes are about 14 feet wide. Thus, vehicle A travelled 25 - 28 feet and vehicle B travelled 6 - 8 feet. Question 1: if both cars entered the intersection at the same time, is it reasonable that one vehicle would be able to accelerate 3 - 4 times and achieve an average velocity of 3 - 4 times that of the other vehicle in this distance?

    Second question: How does the force calculations play into this? It seems that if both vehicles entered the intersection at the same time, from the position of the crash, vehicle A had to achieve higher acceleration than vehicle B. Vehicle A has a higher mass than vehicle B. Thus, it seems if vehicle B has a lower acceleration and lower mass, vehicle B would not have been able to drive vehicle A into vehicle C with the force that occurs. This does not even consider the friction that must be overcome of vehicle A tires with the road.

    My conclusion is that vehicle A must have entered the intersection first, and vehicle B must have had a higher acceleration at time of impact.

    Is my analysis and conclusion sound? What elements have I missed? I'm not looking for accident reconstruction or an expert witness, just an idea if my ideas are sound, and possibly a way to present them. Insurance company is placing 50% blame on both vehicles A and B.
  2. jcsd
  3. May 11, 2006 #2
    Your analysis sounds fair except that you seem to be blurring the line between velocity and accelerarion. Maybe that is just the way I read it, I wonder what others think.
  4. May 12, 2006 #3


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    Made it throug 3/4 of the intersection before getting hit in the rear quarter?
    I think I'd be looking for a lawyer
  5. May 12, 2006 #4
    It very much sounds as if vehicle B did not stop at the intersection, and impacted vehicle A with far more velocity than could have been acquired by accelerating from a standing start for six to eight feet.

    A typical vehicle will accelerate at about 2.5 meters per second, quite a lot less than g. Which means vehicle B ought to have been accelerating for about a second. Which means it should have been travelling at say 2.5 meters per second at time of impact. Call it 8 feet per second. And since 44 feet per second is 30mph, that's 5mph.

    Don't think so.

    Formulae: http://www.stvincent.ac.uk/Resources/Physics/Speed/speed/formulae.html [Broken]
    Last edited by a moderator: May 2, 2017
  6. May 12, 2006 #5


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    Did vehicles A and C impact head-on, and what kind of car is C? If A and C hit head-on, all that was required from B was to alter A's path enough to make it hit C. Ie, the momentum of B isn't what caused the damage to C.....if I'm understanding your scenario correctly.
  7. May 12, 2006 #6
    Thanks for the feeback. I apologize if the scenario is a little confusing.

    Russ: Vehicle A was struck in the rear wheel area of the passenger side by the front end of vehicle B. Vehicle A was rotated by the force, striking vehicle C's front end with the rear wheel area of the driver's side of vehicle A. Vehicle C was a comapct size vehicle.

    Farsight, I did not quite understand exactly what you were trying to explain to me. Could you expound or reword slightly? Thanks
  8. May 15, 2006 #7
    vman: If vehicle B only travelled 6 to 8 feet from a standing start it should have been going really slow when it hit vehicle A. From your description of the accident it hit real hard. So I think it didn't stop at the intersection, and drove straight into your wife.

    A car that can do 0 to sixty in 6.7 seconds is a fast car. And that works out at an acceleration of only 4 metres per second per second. If Vehicle B travelled only two metres before hitting your wife from a standing start, it could have only been going for half a second, and would have been doing 2 metres per second.

    That's about 7 feet per second, and since 44 feet per second = 30mph, it translates into 5mph.
  9. May 15, 2006 #8
    Thanks for all the replies. Do you have any suggestions as to how best present this to the insurance adjusters and their managers? I need to be clear and succinct, but also very elementary, as they do not seem to understand the relationships of the distance traveled, the elapsed time, and the force of the impact. To me, a simple diagram showing the layout of the intersection with the starting positions, the position at impact, and the positions at impact with the 3rd car along with the distance travelled and the simple formulas is easy to follow. Do you think that is a good approach? Again, in the grand scheme of things, this is not a huge deal. Not enough to hire a lawyer or an investigator/witness. But, important enough that I make sure they understand the physics and consider them in their determination. Thanks for any advice. John
  10. May 15, 2006 #9
    I meant to add that I could add an attachment with a diagram if that is of interest.
  11. May 17, 2006 #10
    You've got to say the other car couldn't have been stopped at the intersection like your wife was, so it's his fault. Especially since he hit your wife. Add that his car would have been going at only 2 metres per second if it had been accelerating at 4 meters per second per second for two metres, and this is 5mph which is clearly contradicted by the damage sustained. And his recollection must therefore be "faulty".
  12. May 17, 2006 #11
    Thanks. The wife's mini van is speced at 0 - 60 mph in 8.5 seconds, so likewise, if both cars started at the same time, she could not have gotten through the intersectuion any too fast, even if she floored it and held it.
  13. May 17, 2006 #12


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    Russ' analysis still makes the most sense to me.

    A had lots of speed at the instant it was hit. B only needed enough speed to get A to spin. Once it did that, it was predominantly A's momentum that totaled C. So, it would seem that the scenario is possible even if A and B started at about the same instant.

    I think the clincher will merely be the fact that A was hit on the side, not B - to say nothing of the fact that the hit was at the very rear end - but I'm not sure exactly what the law says about this.

    PS : Going at close to the rated acceleration limit (as speced above), A takes about 4 secs to cover 28 feet. That's ample time for B to realize what's happening, hit the brakes and avoid collision. Seems like B would have a hard time explaining "itself".
    Last edited: May 17, 2006
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