The minimum distance required to stop a car moving at 46.0 mi/h is 39.0 ft. What is the minimum stopping distance for the same car moving at 80.0 mi/h, assuming the same rate of acceleration?
Can I do a proportion or is this totally different?
I assume they mean the rate of DEceleration is the same. The time required to stop will then be larger by a ratio 80/46. Stopping distance is proportional to time x (average velocity), or (80/46)^2.
That makes the answer 39 ft x (40/23)^2
To solve this problem, you can use the concept of proportional reasoning. The minimum stopping distance of a car is directly proportional to its initial speed. Therefore, if you know the ratio of the initial speed to the stopping distance for one situation, you can use that ratio to find the stopping distance for another situation.
Let's assign variables to the given values. We'll use:
v1 = initial speed of the car (46.0 mi/h)
d1 = stopping distance at v1 (39.0 ft)
v2 = new initial speed of the car (80.0 mi/h)
d2 = stopping distance at v2 (which is what we want to find)
Now, let's set up the proportion:
(v1 / d1) = (v2 / d2)
Substituting the given values:
(46.0 mi/h / 39.0 ft) = (80.0 mi/h / d2)
To solve for d2, we can cross-multiply and isolate it:
(46.0 mi/h)(d2) = (39.0 ft)(80.0 mi/h)
(d2) = (39.0 ft)(80.0 mi/h) / (46.0 mi/h)
(d2) = (39.0 ft)(80.0 / 46.0)
Now we can calculate d2:
(d2) = (39.0 ft)(1.7391...)
(d2) ≈ 67.775 ft
Therefore, the minimum stopping distance for the same car moving at 80.0 mi/h, assuming the same rate of acceleration, is approximately 67.775 ft.