The distance required for a car to stop is directly proportional to the square of its velocity. If a car can stop in 112.5 meters at 15 kilometers per hour, how many meters are needed to stop at 25 kilometers per hour?
d = k v^2
112.5 = k (225)
k = .5
so
d = .5 v^2
d = .5 (625) = 312.5
To solve this problem, we need to use the given information about the relationship between distance and velocity. The problem states that the distance required for a car to stop is directly proportional to the square of its velocity.
Let's define some variables:
- Let d represent the distance required to stop at a given velocity.
- Let v represent the velocity of the car.
The relationship can be expressed as: d = k * v^2, where k is the constant of proportionality.
Now, let's use the given information to solve for k. We are given that the car can stop in 112.5 meters at 15 kilometers per hour:
112.5 = k * (15^2)
First, convert the velocity from kilometers per hour to meters per hour:
15 kilometers per hour = 15 * 1000 meters per hour = 15000 meters per hour.
Now, substitute the values into the equation:
112.5 = k * (15000^2)
Next, solve for k:
k = 112.5 / (15000^2)
Once we have the value of k, we can use it to determine the distance required to stop at 25 kilometers per hour.
First, convert the velocity from kilometers per hour to meters per hour:
25 kilometers per hour = 25 * 1000 meters per hour = 25000 meters per hour.
Now, substitute the values into the equation:
d = k * (25000^2)
Finally, calculate the distance:
d = k * (25000^2)
d = (112.5 / (15000^2)) * (25000^2)
Using a calculator, we can solve this equation to find the distance required to stop at 25 kilometers per hour.