Financial Algebra© Cengage/South-Western Slide 11

5-9

ACCIDENT INVESTIGATION DATA

5-9

ACCIDENT INVESTIGATION DATA

Determine the minimum skid speed using the skid mark formula.

Determine the minimum skid speed using the yaw mark formula.

OBJECTIVES

Financial Algebra© Cengage Learning/South-Western Slide 22

Accident reconstructionistKnowledge of both math & CSI

skid markRoad mark when tire is lockedLight at 1st, then darkens until stop

or collision shadow skid mark

The light part of the skid mark when driver 1st applies brakes

anti-lock braking system (ABS)Does not allow wheels to lock

continuously; brakes pulse & skid marks are uniform dashes

skid speed formula, for straight skid marks

drag factor, fPull of the road on tires;

different surfaces create differing friction amounts

braking efficiency, nA decimal # pertaining to the

condition of the front & rear brakes

Key Terms

efficiency brakingn factor, dragf

distance skidD speed, S

30DfnS

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skid distance, D, of straight skid marks A function of the # of skid marks and their lengths If 4 marks of equal length are present, then that amount is used for D in the skid

speed formula If the skid marks are of different length, or there are fewer than 4 marks, then the

average of the lengths is used in the formula If only 1 skid mark is present, then that length is used in the formula

yaw mark Curved skid mark from vehicle slipping sideways while continuing forward

skid speed formula, for yaw marks Chord

The line segment that connects two points on an arc of a yaw mark

middle ordinate The short line segment from the perpendicular bisector of the chord to the arc

Key Terms

arc of radiusr factor, dragf

speed, minimum S

15frS

length ordinate middle length, chord 28

2

MCM

M

Cr

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Example 1Example 1Example 1Example 1

A car is traveling on an asphalt road with a drag factor 0.78. The speed limit on this portion of the road is 35 mi/h. The driver just had his car in the shop and his mechanic informed him that the brakes were operating at 100% efficiency. The driver must make an emergency stop, when he sees an obstruction in the road ahead of him. His car leaves four distinct skid marks each 80 feet in length.

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Example 1Example 1Example 1Example 1drag factor is f = 0.78, braking efficiency is n = 1, skid distance is D = 80, speed limit is 35 mphWhat is the minimum speed the car was traveling when it entered the skid? Round your answer to the nearest tenth.

Was the driver exceeding the speed limit when entering the skid?

130x80x.78xS 1,872S mph 43.3S

Yes, the driver was speeding & could be fined.

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Example 2Example 2Example 2Example 2

Melissa was traveling at 50 mi/h on a concrete road with a drag factor of 1.2. Her brakes were working at 90% efficiency. To the nearest tenth of a foot, what would you expect the average length of the skid marks to be if she applied her brakes in order to come to an immediate stop?

90213050 ..D

D4.3250

22 4.3250 D

D4.322500 D2.77

Under the given conditions, you would expect the average of the skid marks to be about 77.2 feet.

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EXAMPLE 3EXAMPLE 3EXAMPLE 3EXAMPLE 3 An accident reconstructionist took measurements from yaw

marks left at a scene. Using a 43-foot length chord, she determined that the middle ordinate measured approximately 4 feet. The drag factor for the road surface was determined to be 0.8. Determine the radius of the curved yaw mark to the nearest tenth of a foot. Determine the minimum speed that the car was going when the skid occurred to the nearest tenth.

4

= 43

28

2 M

M

Cr

ftr 8.59232

432

mph 26.8 8.598.015S

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Determine the minimum speed of a car at the point the brakes are immediately applied to avoid a collision based upon a yaw mark chord measuring 62.4 feet and a middle ordinate measuring 5 feet. The drag factor of the road surface is 1.2. Round your answer to the nearest tenth.

CHECK YOUR UNDERSTANDING

f = 1.2, M = 5, C = 62.4, find r and then S

mphS 4.428.992.115

ft.r 899

2

5

40

4.62 2