Asked by Halima Soliman on May 29, 2024
Verified
The stopping distance d of an automobile is directly proportional to the square of its speed s . On a road surface, a car requires 787878 feet to stop when its speed is 252525 miles per hour. The brakes are applied when the car is traveling at 303030 miles per hour under similar road conditions. Estimate the stopping distance to the nearest foot.
A) 123.5123.5123.5 feet
B) 178.2178.2178.2 feet
C) 112.3112.3112.3 feet
D) 3.73.73.7 feet
E) 101.1101.1101.1 feet
Directly Proportional
A relationship between two variables where their ratio is constant.
Stopping Distance
The total distance a vehicle travels from the point when the driver first perceives a need to stop, to when the vehicle comes to a complete halt.
- Comprehend and utilize equations to determine stopping lengths and generated power under diverse circumstances.
Verified Answer
SM
Sarah MagdyJun 03, 2024
Final Answer :
C
Explanation :
We know that stopping distance, d is directly proportional to the square of speed, s. This can be written as:
d=k*s^2
where k is the constant of proportionality.
To find k, we can use the given information that the car requires 78 feet to stop when its speed is 25 miles per hour:
78=k*25^2
k=78/625
k=0.1248
Now we can use this value of k to estimate the stopping distance when the car is traveling at 30 miles per hour:
d=0.1248*30^2
d=112.3 feet
Therefore, the answer is C, 112.3 feet, rounded to the nearest foot.
d=k*s^2
where k is the constant of proportionality.
To find k, we can use the given information that the car requires 78 feet to stop when its speed is 25 miles per hour:
78=k*25^2
k=78/625
k=0.1248
Now we can use this value of k to estimate the stopping distance when the car is traveling at 30 miles per hour:
d=0.1248*30^2
d=112.3 feet
Therefore, the answer is C, 112.3 feet, rounded to the nearest foot.
Learning Objectives
- Comprehend and utilize equations to determine stopping lengths and generated power under diverse circumstances.
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