18

CHAPTER

MATHEMATICS

IN ENGINEERING

Stopping Stopping

Sight Sight

Speed Speed Distance Speed Speed Distance

(mph) (ft /s) (ft) (mph) (ft /s) (ft)

0 0.0 0 45 66.0 370

5 7.3 21 50 73.3 436

10 14.7 47 55 80.7 508

15 22.0 78 60 88.0 584

20 29.3 114 65 95.3 666

25 36.7 155 70 102.7 753

30 44.0 201 75 110.0 844

35 51.3 252 80 117.3 941

40 58.7 309

Stopping Sight Distance (ft)

1000

900

800

700

600

500

400

300

200

100

0

0 20 40 60 80 100 120

Speed (ft/s)

I

n general, engineering problems

are mathematical models of

physical situations. For example,

a model known as stopping sight

distanceis used by civil engineers

to design roadways. This simple

model estimates the distance a

driver needs in order to stop his

car traveling at a certain speed

after detecting a hazard. The

model proposed by the American

Association of State Highway and

Transportation Officials (AASHTO)

is given by

where

Sstopping sight distance (ft)

Vinitial speed (ft/s)

gacceleration due to gravity,

32.2 ft/s

2

fcoefficient of friction

between tires and roadway

Ggrade of road

Tdriver reaction time (s)

a

%

100

b

S

V

2

2 g 1 fG 2

T V

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