The braking distance of a car varies directly as the square of the speed. If braking distance of a certain car is 49 feet at 30 mph, find the approximate braking distance at 65 mph
well, around four times :)
d = k v^2
49 = k (900)
k = 49/900
d = (49/900)(65)^2 = 230 feet
To find the approximate braking distance at 65 mph, we first need to set up a proportional relationship equation using the given information.
We are told that the braking distance of a car varies directly as the square of the speed. Let's denote the braking distance as D and the speed as S.
This can be written as: D ∝ S^2
Since we are looking for an approximate braking distance, we can use this proportional relationship to find the constant of variation.
Let's use the first given data point: a braking distance of 49 feet at 30 mph.
So, we have the equation: 49 ∝ 30^2
Now, we can solve for the constant of variation (k) by dividing both sides of the equation by the value of the speed squared:
49 / (30^2) = k
k ≈ 0.05411
Now that we have the value of the constant of variation (k), we can use it to find the approximate braking distance at 65 mph.
Let's substitute the values into the proportional relationship equation:
D ∝ S^2
D ≈ k * 65^2
D ≈ 0.05411 * 65^2
Calculating this gives us:
D ≈ 222.4875
Therefore, the approximate braking distance at 65 mph is approximately 222.49 feet.