## The distance it takes stop a car varies directly at the square of the sure of the car. If it takes 112 feet for a car traveling at 40mph to

Question

The distance it takes stop a car varies directly at the square of the sure of the car. If it takes 112 feet for a car traveling at 40mph to stop, what distance is required for a speed of 59 mph?

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1 week 2021-10-13T02:18:50+00:00 1 Answer 0

1. The distance required for a speed 59 mph is 243.67 feet

Step-by-step explanation:

The direct variation is a relation ship between two quantities, the

ratio between them is constant

• If y varies directly with x, then y = k x
• x is the constant of variation
• To find k substitute y and x by their initial values

∵ The distance it takes stop a car varies directly at the square

of the speed of the car

∴ d = k v², where d is the distance in feet and v is the speed in mph

∵ it takes 112 feet for a car traveling at 40 mph to stop

∴ d = 112 feet , v = 40 mph ⇒ initial values

– Substitute these values in the rule above to find k

∵ 112 = k (40)²

∴ 112 = 1600 k

– Divide both sides by 1600

∴ k = 0.07

∴ d = 0.07 v² ⇒ equation of variation

∵ The speed v = 59 mph

– To find the distance required for this speed substitute v in

the equation of variation by 59

∵ d = 0.07 (59)²

∴ d = 243.67 feet

The distance required for a speed 59 mph is 243.67 feet