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
Learn more:
You can learn more about variation in brainly.com/question/10708697
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