Including reaction time, the stopping distance is more than 20 feet at 10 miles per hour. At 20 miles per hour it will be about:
A. 30 feet
B. 63 feet
C. 40 feet
D. 75 feet
Answer (1)
Assume stopping distance d is proportional to the square of the speed v : d = k v 2 .
Use the given information ( 20"> d > 20 feet at v = 10 mph) to estimate k ≈ 0.21 .
Calculate the stopping distance at v = 20 mph: d = 0.21 × ( 20 ) 2 = 84 feet.
Choose the closest answer from the options: 75 f ee t .
Explanation
Understanding the Problem We are given that the stopping distance is more than 20 feet at 10 miles per hour. We need to estimate the stopping distance at 20 miles per hour.
Setting up the Model Let's assume that the stopping distance is proportional to the square of the speed. This is a common approximation in physics.
Defining the Relationship Let d be the stopping distance and v be the speed. Then we can write the relationship as: d = k v 2 where k is a constant of proportionality.
Estimating the Constant of Proportionality We are given that 20"> d > 20 when v = 10 . Let's use d = 21 to estimate k :
21 = k ( 10 ) 2 k = 100 21 = 0.21
Calculating the Stopping Distance at 20 mph Now we can use this value of k to estimate the stopping distance at v = 20 :
d = 0.21 ( 20 ) 2 = 0.21 × 400 = 84 So the stopping distance is approximately 84 feet.
Choosing the Closest Answer Looking at the answer choices, the closest value to 84 feet is 75 feet.
Examples
Understanding stopping distances is crucial for road safety. For instance, knowing how quickly a car can stop at different speeds helps in maintaining safe following distances. This concept applies directly to real-world scenarios such as driving in urban areas, on highways, or in adverse weather conditions, where reaction time and braking efficiency are critical for preventing accidents. The relationship between speed and stopping distance, often approximated as proportional to the square of the speed, allows drivers to make informed decisions and adjust their driving behavior accordingly.
