Discovery Activity 12: Speed and Stopping Distance
Suppose while driving you see the brake lights of the car in front of you come on. If you assume
the car ahead is going to stop and your brakes must be applied, then how far will your car travel
before it comes to a stop? In other words, what is the stopping distance from the moment your
brain receives the signal to brake until the car is no longer moving?
The table below contains data on this situation. Note that the total stopping distance is the sum
of the reaction distance (distance traveled from the time you realize that you must brake until the
brakes are applied) and the braking distance (distance traveled after the brakes are applied).
Average Stopping Distance of Cars on Dry Level Pavement
Reaction
Braking
Total Stopping
Distance
Distance
Distance
(feet)
(feet)
(feet)
10
11
6
17
20
22
25
47
30
33
55
88
40
44
105
149
50
55
188
243
60
66
300
366
70
77
455
532
Stopping distances are based on tests made by U.S. Bureau of Public Roads.
Driver reaction distance is based on the reaction time of
second.
Speed
(mph)
a. Observe the pattern of the quantities in first two columns of the table above. What type of
function exhibits this pattern? Explain.
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b. Find an equation that gives the reaction distance R (in feet) as a function of the speed x (in
miles per hour). Hint: Find the slope, m, and y-intercept, b, and then put in form
.
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c. Enter the data from table columns 1 and 3 into your graphing calculator and plot the data
with speed as the input or independent variable and braking distance as the output or
dependent variable. Observe the pattern of the data points and then explain what type of
function might be a good model for the data?
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d. Use the (quadratic) regression feature of your graphing calculator to find a symbolic model
or equation giving braking distance B as a function of the speed x. Round a, b, and c to the
thousandths place.
e. Since total stopping distance is the sum of reaction distance and braking distance, use the
equations in parts b and d to find an equation that gives total stopping distance T as a
function of speed x.
f. Create a table for the braking distance function B and the total stopping distance function T.
Round to the nearest foot.
Speed
(mph)
Braking Distance
(feet)
Total Stopping Distance
(feet)
10
20
30
40
50
60
70
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g. Use the table in part f to construct a graph for the total stopping distance function T. Label
and scale each axis and place an appropriate title at the top, center of the graph.
h. Observe the graph in part g and then explain the relationship between speed and stopping
distance as speed increases.
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i. What is the total stopping distance for a car traveling at 75 mph? Round to the nearest foot.
j. Based on skid measurements at an accident scene, a car’s total stopping distance is 160 feet.
Use your graphing calculator to estimate the speed of the car to the nearest mph.
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