The distance require to stop a car varies directly as the square of its speed. If 250 feet are required to stop a car traveling 60 miles per hour, how many feet are required to stop a car traveling 96 miles per hour!
x = 640
To solve this problem, we can use the concept of direct variation. Let's first define the variables:
Let D be the distance required to stop the car.
Let V be the speed of the car.
According to the problem statement, the distance required to stop the car varies directly as the square of its speed. This can be written as:
D = k * V^2 (equation 1)
where k is the constant of variation.
Now, let's use the given information to find the value of k. We are given that when the car is traveling at 60 miles per hour, the distance required to stop is 250 feet.
So, plugging these values into equation 1, we get:
250 = k * 60^2
Simplifying, we have:
250 = k * 3600
Now, let's solve for k:
k = 250 / 3600
k ≈ 0.0694
We have found the value of k as approximately 0.0694.
Now, we can use equation 1 with the new speed value (96 miles per hour) to find the distance required to stop the car:
D = 0.0694 * 96^2
Calculating this expression, we have:
D ≈ 603.34
Therefore, approximately 603.34 feet are required to stop a car traveling at 96 miles per hour.
To solve this problem, we can use the concept of direct variation. Direct variation states that when two variables are directly proportional, their ratio remains constant. In this case, the distance required to stop a car is directly proportional to the square of its speed.
Let's define the variables:
Let "d" represent the distance required to stop the car.
Let "s" represent the speed of the car.
According to the problem, we have the following information:
For a car traveling 60 miles per hour, the distance required to stop is 250 feet.
We can set up a proportion to solve for the constant of variation:
d/250 = s^2/60^2
Now, we can substitute the given values into the equation:
d/250 = (96^2)/(60^2)
To solve for "d", we can cross-multiply and then divide:
d = (250 * (96^2)) / (60^2)
Using a calculator, we can simplify the expression and find the value for "d":
d ≈ 949.44 feet
Therefore, approximately 949.44 feet are required to stop a car traveling 96 miles per hour.
250/(60)^2 = x/(96^2)
Solve for x.