The stopping distance (s) of a car varies directly as the square of its speed (v). If a car traveling at 50 mph requires 170 ft to stop, find the stopping distance for a car traveling at
v2 = 55
mph.
we have s = kv^2
That is, s/v^2 is constant. So, now we know that
170/50^2 = x/55^2
Note that we don't really need to know the value of k, just that it is constant.
To find the stopping distance for a car traveling at 55 mph, we can use the given information that the stopping distance (s) varies directly as the square of the speed (v).
Mathematically, this can be represented as s = kv^2, where k is the constant of variation.
We are given that when the speed is 50 mph, the stopping distance is 170 ft. Let's use this information to find the value of k.
Substituting the given values into the equation:
170 = k(50)^2
Simplifying:
170 = k * 2500
170 / 2500 = k
0.068 = k
Now that we have the value of k, we can substitute it into the equation to find the stopping distance for a car traveling at 55 mph.
s = 0.068 * (55)^2
s = 0.068 * 3025
s ≈ 205.4 ft
Therefore, the stopping distance for a car traveling at 55 mph is approximately 205.4 ft.
To find the stopping distance for a car traveling at 55 mph, we first need to determine the relationship between the stopping distance (s) and the speed (v) of the car.
We are given that the stopping distance varies directly as the square of the speed. This can be represented as:
s = k * v^2
where k is the constant of variation.
To find the value of k, we can use the given information that a car traveling at 50 mph requires 170 ft to stop:
170 = k * (50)^2
170 = k * 2500
k = 170 / 2500
k = 0.068
Now that we have the value of k, we can substitute it back into the equation to find the stopping distance for a car traveling at v = 55 mph:
s = 0.068 * (55)^2
s = 0.068 * 3025
s ≈ 205.4 ft
Therefore, the stopping distance for a car traveling at v = 55 mph would be approximately 205.4 ft.