Precalculus Speed and skid marks word problem Police estima

Precalculus - Speed and skid marks word problem?

Police estimate that the speed s of a car in miles per hour varies directly as the square root of d, where d in feet is the length of the skid marks left by a car traveling on a dry concrete pavement. A car traveling 48 miles per hour leaves skid marks of 96 feet.

A. Write an equation relating s and d

B. Use the equation in part A. to estimate the speed of car whose skid marks stretched (i) 60, (ii) 150 feet, and (ii) 200 feet.

C. Suppose you are driving 70 miles per hour and slam on your brakes. How long will you skid marks be?

Solution

A) speed s of a car in miles per hour varies directly as the square root of d

s= kd

k is constant of proportion

car traveling 48 miles per hour leaves skid marks of 96 feet.

48 =k(96)

k=48/(96)

k=26

s=(26)d is the equation

B)i)d =60 ft

s=(26)60

s=38 miles per hour

ii)d =150 ft

s=(26)150

s=60 miles per hour

iii)d =200 ft

s=(26)200

s=69.3 miles per hour

c)s=70 miles per hour

s=(26)d

70=(26)d

d=70/(26)

d=[70/(26)]²

d=204.2ft