# math

The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car traveling 40 mph can stop in 100 ​ft, how fast can a car travel and still stop in 256 ​ft?

1. 👍
2. 👎
3. 👁
1. Just translate ...

d = k(r^2) , where k is a constant
plug in the given to find k

100/5280 = k(1600)
k = (100/1600)/(5280) = 1/84480

d = (1/84480)r^2
if d = 256 ...
256/5280 = (1/84480)r^2
84480(256)/5280 = r^2

256(16) = r^2

r =16(4)
= 64 mph

notice we could have skipped the 5280 ft to mile conversion, since in both cases the same units were used. e.g. mph <---> ft

.........................

we could have used a simple ratio:

d1/d1 = (r1)^2/(r2)^2

100 ft/256 ft = (40 mph)^2/ (r2)^2
25/64 = 1600/r2^2
take √ of both sides
5/8 = 40/r2
5r2 = 320
r2 = 64

1. 👍
2. 👎
2. Where does the 5280 come from?

1. 👍
2. 👎

## Similar Questions

1. ### math

If a car is speeding down a road at 40 (mph), how long is the stopping distance compared to the stopping distance if the driver were going at the posted speed limit of 25 ? Express your answer as a multiple of the stopping

2. ### Physics

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.6 m/s2 for 4.5 seconds. It then continues at a constant speed for 7.3

3. ### physics

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.6 m/s2 for 4.4 seconds. It then continues at a constant speed for 8.5

4. ### Math

the stopping distance of an automobile is directly proportional to the square of its speed v. a car required 90 feet to stop when its speed was 70 miles per hour. find a mathematical model that gives the stopping distance d in

1. ### physics

A car is traveling at Vx =20 m/s. The driver applies the brakes, and the car slows with ax = -4m/s^2. What is the stopping distance

2. ### physics

A car starts from rest and travels for t1 seconds with a uniform acceleration a1. The driver then applies the brakes, causing a uniform acceleration a2. If the brakes are applied for t2 seconds, determine the following. Answers

3. ### Physics

A race car can be slowed with a constant acceleration of -11 m/s^2 a. If the car is going 55 m/s, how many meters will it travel before it stops? b. How many meters will it take to stop a car going twice as fast? According to one

4. ### Mechanics NYA

Assume you are driving a car at a constant speed of 75.0 km/h. Suddenly you see a deer standing on the highway and you must put on the brakes. Your reaction time (time elapsed between the moment you see the deer and your foot

1. ### physics

A car is traveling at v = 16m/s . The driver applies the brakes and the car decelerates at a= -4.0 m/s^2 . What is the stopping distance?

2. ### Math algebra

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?

3. ### Physics

A car is initially travelling at a constant speed of 20 m/s along a highway. Suddenly, the driver applies the brakes, causing the car to accelerate at -5.0 m/s^2. If the driver applied the brakes 0.50s late, determine the distance

4. ### science

The driver of a 1.00X103 kg car traveling on the interstate at 35.0 m/s slams on his brakes to avoid hitting a second vehicle in front of him, which had come to rest because of congestion ahead. After the brakes are applied, a