Problema Solution
The braking distance D in feet required to stop a car traveling x mph on dry, level pavement can be approximated by D=1/9x^2.
(a.) Calculate the braking distance for 20 mph and 70 mph. how do your answers compare?
(b.) If the braking distance is 49 feet, estimate the speed of the car.
(c.) Use a calculator to solve part (b) numerically. Do your answers agree?
Answer provided by our tutors
The breaking distance formula is: D = (1/9)x^2
(a.) For x = 20 mph the breaking distance is:
D = (1/9)*20^2
D = 400/9
D = 44.44 ft
For x = 70 mph the breaking distance is:
D = (1/9)*70^2
D = 4900/9
D = 544.44 ft
544.44 - 44.44 = 500
The breaking distance for 70 mph is 500 ft longer that the breaking distance for 20 mph.
(b.) In this case D = 49 ft and we need to find x:
(1/9)x^2 = 49
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click here to see the equation solved for x
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x = 21 mph
The speed of the car is 21 mph.