A car is sitting at a red light and is rear-ended by a second car. 
The second car pushes the first car approximately 300 feet after
impact.  How many miles per hour was the second car going?

If I cant get an exact answer I would welcome any "educated guesses." 
I was the person in the first car that was hit and I would like to
know this information.

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Request for Question Clarification by tutuzdad-ga on 10 Oct 2006 20:00 PDT

Dear sealsly-ga; 

Honestly there are far too many variables to make much of an
"educcated guess". Because of that I will offer you this FIRST and let
YOU decide if it is worthy of consideration. Without knowing the
various environmental and roadway factors it is virtually impossible
for anyone to answer your question definitively. As a trained accident
investigator myself I can confidently say that the based on your
description of what took place the best you could hope for is a ball
park guess from ANYONE.

You see, each accident has its own characteristics and these
characteristics, whcn taken into account individually or combined, is
what often (but not always) creates a relatively predictable scenario.
A number of issues can have a dramatic impact (no pun intended) on the
way in which an collision evolves. Some of the more important issues
are:

Vehicle weight (year, make, model, engine size, etc)

The drag factor and the coefficient of friction (the physics that
affects the way in which the vehicles? tires grip the surface and the
mathematical formula that can closely determine how profound or how
liberal the drag factor might have been)

The weather (ice, snow, heat, water, etc.)

The pre-collision condition of the vehicles (most importantly the
condition of both vehicles? tires and brakes)

The presence, depth, width, and direction of yaw marks (skids), post
impact slide, falls, flips, vaults, (or flips ?and? vaults, which are
calculated differently in some instances and in others are combined or
"gathering" speeds).

And finally the testimony of the drivers (Did the impacted driver
apply the brakes and for how long? Did the impacting driver apply his
brakes? etc)

These are only a few examples of the many issues an investigator uses
to help determine how fast a vehicle is traveling at impact. But keep
in mind that no investigator ? no matter how clever he says he is ?
can tell you exactly how fast a vehicle was traveling. The best
accident reconstructionists can sometimes provide the smallest range
of possibilities using known data applied to a proven algorithm but
this is only in excellent case scenarios and certainly not based on
sketchy information alone.

With at in mind one can apply the formula: Speed = sqrt(30 x CD x
Length) [where ?CD? is ?roadway conditions? and ?Length? is the
?length of skid?) which can provide a rough estimate of the impacting
vehicle?s speed based on skid marks alone. This will produce an
?estimate? of the speed assuming the impacted vehicle is stationary,
the drag factor of the surface is consistent with that of new, dry
asphalt AND that the impacted vehicle (with brakes applied) left 300
feet of skid marks. Now I understand that these are probably not all
an accurate depiction of what took place but just to give you some
idea (educated guess, as you put it), the speed of the impacting
vehicle may have been roughly 91.5 mph (147 kph) at the time of
impact.

I came to this conclusion using a CLAIMSTAR impact calculator

CLAIMSTAR
http://www.claimstar.net/main.taf?p=9,4

You might also have some luck with these calculators, the latter of
which requires more detailed input which you may have at your
disposal:

CLAIMS PAGES
http://www.claimspages.com/tools/skidspeed.asp?catid=1&cat=Automotive

GREATRIX
http://www.greatrix.co.uk/AICalculator.html

All these tools offer the same disclaimer I warned about, they ?should
not be used as a substitute for a proper accident reconstruction
investigation.? This answer merely reflects the rough estimate you
requested. The caveat here of course is that if your vehicle laid down
less skid in response to the impact the speed of the impacting vehicle
was likely less than what I have indicated, but this should give you a
very good idea of what speeds you can expect.

The intent of these calculators is not to measure the speed based on
the transfer rate of speed at impact, rather they are designed to show
the speed of the original vehicle when THAT vehicle leaves 300 feet of
skid marks. With that said, here is a chart that may more accurately
illustrate the speed of the vehicle you described.

http://www.e-z.net/~ts/speedch.htm
  
Taking into account the transfer of velocity, the post impact skid of
the vehicle and the post impact slide, and assuming the vehicle that
hit you left 60 feet of straight-line skid or post impact slide marks,
it would be safe to assume that the impacting vehicle was traveling at
a most probable speed range of about 30-40 mph (48-64 kph). This, I
believe, is a more likley scenario. While it seems relatively low in
comparison to the earlier scenario, a 30-40 mph straigh-line collision
is actually a tremendous impact and quite capable under certain
conditions of causing the transfer of velocity to the degree you
described.

Please let me know if this is suitable to you as an answer, as
?educated guesses? go.

Regards;
Tutuzdad-ga

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Clarification of Question by sealsly-ga on 10 Oct 2006 21:02 PDT

Thank you for your well thought out answer.  I didnt realize there
where so many variables involved.  I appreciate your time and this is
a suitable answer.  Thanks again.

Dear sealsly-ga:

Thank you for allowing me to answer your question. In order to
officially close your question I am simply referring you to my earlier
post. I look forward to your final rating and comments.

Best regards;
tutuzdad-ga

provided helpful links and plenty of info

The approximate weights of the two vehicles?
Was the stationary car in forward gear, or in neutral, or in "park" gear?
Did this occur on a totally level surface, or was there an uphill or downhill grade?

dont really know the approx weights.  but the car that was hit was a
2003 toyota echo and the car that rear-ended me was a 1997 volvo
(sedan type, 4 door, not sure of the exact model).
 
the sationary car was in drive gear with a brake on at a red light.

totally level surface.

The position of the Volvo after the accident is more telling than
where the Toyota ended up. The Toyota's travel has too many variables,
primary of which is were the brakes maintained the whole time (not
likely).

The Volvos for 1998 clocked in around 1700 kilos and the 2003 Echo was
a bit under 1000 kilos, curb weights. Loaded you can probably figure
the Volvo is 1850 and the Echo 1075. It might be easier to do the
calculations for 2000 and 1000 kilos to get a nice thumbnail idea.

Good luck with the math! I'm terrible at it-- that's why I became a vet.   ;-)

Good answer tutuzdad.

Yes, very interesting.  300 ft is quite a distance, suggesting that
the impacted driver's foot slipped off the brake - or rose up under
the force of the initial impact.

Don't most (or all) newer model cars have recording devices that allow
authorities or experts to know exactly the speed a car was travelling
at the point of impact as well as other factors such as if the driver
ever applied the brakes before the accident?  I have family members
who were involved in an extremely serious accident and they were able
to determine from the "black box" the exact speed of the car at the
moment of impact and for how long the driver applied the brakes before
the impact.

i was in the process of posting a comment last night when tutuzdad
locked the question.  if i were smart i would keep that to myself, as
i was going to say that 300 ft (a football field!) just couldn?t
possibly be right.  i guess i was wrong; as someone who has exactly
zero years of law enforcement experience, i defer to tutuzdad?s
knowledge in such things, but i?m still left with two thoughts.

first, as myoarin said, i have to believe the brakes were not being
applied after the first 0.05 seconds, and in addition i think the car
couldn?t have been in gear.  surely it rolled much of that 300 ft. 
were there really 300 ft of skid marks from the echo?s tires?

second, do i understand you were in the car when this happened?! 
seatbelts and airbags are great and all, but i just can?t believe
someone would survive a 90mph straight-on collision (and in an echo no
less!).

if the brakes were off and it wasn?t in gear, the difference between a
0.1% uphill and 0.1% downhill grade (which would both look level)
would have a huge effect on the length it rolled before stopping.

in any case, congratulations on being alive!

-cab