Assume that the stopping distance of a van varies directly with the sqaure of the speed . A van traveling 40 miles per hour can stop in 60 feet. If the van is traveling 56 miles per hour, what is its stopping distance?
To solve this problem, we can set up a proportion using the variation equation.
The stopping distance (D) varies directly with the square of the speed (S). This can be represented as:
D = k * S^2
We are given that when the van is traveling at 40 miles per hour, the stopping distance is 60 feet. We can use this information to find the value of the constant of variation (k).
60 = k * 40^2
60 = k * 1600
k = 60 / 1600
k = 0.0375
Now that we have the value of k, we can find the stopping distance when the van is traveling at 56 miles per hour.
D = 0.0375 * 56^2
D = 0.0375 * 3136
D = 117.6 feet
Therefore, when the van is traveling at 56 miles per hour, its stopping distance is approximately 117.6 feet.
To solve this problem, we need to find the constant of variation, also known as the constant of proportionality. Let's call it k.
We know that the stopping distance of the van varies directly with the square of the speed. Mathematically, we can express it as follows:
stopping distance = k * speed^2
We are given that when the van is traveling at 40 miles per hour, the stopping distance is 60 feet. So we can substitute these values into the equation:
60 = k * 40^2
Now we can solve for k:
k = 60 / (40^2) = 60 / 1600 = 0.0375
Now that we have the value of k, we can find the stopping distance when the van is traveling at 56 miles per hour. Let's call it sd2:
sd2 = k * speed^2
Substituting the given values:
sd2 = 0.0375 * 56^2
Now we can calculate sd2:
sd2 = 0.0375 * (56^2) = 0.0375 * 3136 = 117.6
Therefore, when the van is traveling at 56 miles per hour, its stopping distance is 117.6 feet.
d = ks^2
So, d/s^2 = k, a constant.
So, you want d such that
d/56^2 = 60/40^2