Math II Unit 1 Project: Full Stop Ahead
What is a safe distance between cars traveling on the highway? After you apply brakes to stop your car, how far will your car travel before coming to a full stop? How do accident investigators determine whether cars involved in accidents were traveling at safe speeds? There are many variables that affect how quickly a car can stop. These variables include the car’s speed, the driver’s reaction time, the type of road, the weather conditions and, of course, the effectiveness of the brakes.As you work through the activities, you will use formulas to estimate safe speeds under various conditions. You will make a graph to illustrate the relationship between speed and stopping distance. Then, you will plan a skit with your classmates to illustrate what you have learned about safe highway driving.
To reduce the likelihood of an accident when driving, you should consider how far your car will travel before safely coming to a stop for the speed at which you are traveling. Assume you are traveling on a dry road and have an average reaction time. The formula d=0.044s2+1.1s gives you a safe stopping distance d in feet, where s is your speed in mi/h. Make a table of values for speeds of 10, 20, 30, 40, 50, and 60 mi/h. Then, graph the function.
S 0.044s^2 + 1.1s D
10 - 0.044(10)^2 + 1.1(10) 15.4
20 - 0.044(20)^2 + 1.1(20) 39.6
30 - 0.044(30)^2 + 1.1(30) 72.6
40 - 0.044(40)^2 + 1.1(40) 114.4
50 - 0.044(50)^2 + 1.1(50) 165
60 - 0.044(60)^2 + 1.1(60) 224.4
Dry Road = Square Root of 27(d)
Wet Road = Square Root of 13.5(d)
60ft = Square Root of 27(60)
Dry Road = 40.249mph
Wet Road = 28.460mph
120ft = Square Root of 27(120)
Dry Road = 56.921mph
Wet Road = 40.429mph
Why do you think the estimates of speed do not double when the skid marks double in length? Based on these results, what conclusions can you make about safe distances between cars?
Speed will not double as the distance does because the speed is only a gradual increase while the distance increases more than the speed does. If two cars ride one behind the other at the same rate of travel in the same conditions and braked at the same time, there wouldn't be a collision, however if driver does not react as quickly as needed then collision is inevitable. In conclusion the appropriate safe distance would be approximately 4.1 - 10ft, 4.1 being the minimum, or 2 car lengths apart to allow a safe stopping distance.
Suppose you are driving on a dry road with 150 ft (about 10 car lengths) between your car and the car in front of you. Use the formula from Activity 1 to find the maximum speed you should be traveling in order to leave a safe stopping distance.
The maximum speed of the vehicle would be 47.2mph in order to stop at 150ft giving approximately .06ft of distance left.