A car with good tire tread can stop in less distance than a car with poor tread. The formula for the stopping distance d, in feet, of a car with good tread on dry cement is approximated byd = 0.04v2 + 0.5v,where v is the speed of the car. If the driver must be able to stop within 59 ft, what is the maximum safe speed, to the nearest mile per hour, of the car?mph

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Asked Nov 24, 2019
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A car with good tire tread can stop in less distance than a car with poor tread. The formula for the stopping distance d, in feet, of a car with good tread on dry cement is approximated by

d = 0.04v2 + 0.5v,

where v is the speed of the car. If the driver must be able to stop within 59 ft, what is the maximum safe speed, to the nearest mile per hour, of the car?
mph

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Expert Answer

Step 1

Given:

The formula for the stopping distance d, in feet, of a car is d = 0.04v2 + 0.5v, where v is the speed of the car.

Step 2

If the driver must be able to stop within 59 ft, then the maximum safe speed would be

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59 0.04v2 0.5v

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Step 3

Multiply the above equation by 100...

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5900 4v2+50v 4v2+50v 5900 = 0 2(2v2+25v-2950)= 0 2v2+25v 2950 0

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