# The Combined Speed Formula

•With a multiple phase accident where a vehicle may
have undergone several speed changing events, it is necessary
to use the combined speed formula (above) to estimate the
original speed of the vehicle.

•If for example, a vehicle looses 30 mph in sliding
before impact, 20 mph in the collision and 10 mph in sliding
to a stop after the impact, the original speed of the vehicle
is then:

S x S = 30 x 30 + 20 x 20 +10 x 10 = 900 + 400 + 100 =
1400, so that S = 37 mph

Notice that we cannot simply add the speed decrements
together, they must be combined using the formula. This
frequently leads to lower speed estimates than might be
anticipated when looking at the various speed numbers before
they are combined. The reason is that speed energy- what's
really being computed in the partial estimates- varies with
the square of the speed. Thus 20 mph is four times the
(kinetic) energy of 10 mph (20 x 20 =400, 10 x 10 =100), not
twice as much. The speed from skid marks formula - S = 5.5 x
sqrt ( cd x distance ) - is a computational aid which assumes
a zero final velocity, that is, that the vehicle has stopped
at the end of the skid marks; if the computed value is to be
taken as the original speed of the vehicle.. It does not
yield speed drops simpliciter. Thus, 20 feet of locked wheel
skid marks represents about 20 mph if the vehicle is stopped
at the end of the marks. Suppose however that the vehicle is
doing 60 mph when it leaves 20 feet of skid marks. Its speed
at this point is:

S = sqrt (3600 - 400) = sqrt 3200 = 56.6 mph
!

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