Braking Distance

Distance to Brake (w/ antilock brakes)

Expression 13: "d" Subscript, "b" , Baseline equals StartFraction, "v" squared Over 2 left parenthesis, "a" minus 9.8sin left parenthesis, StartNestedFraction, "s" pi NestedOver 180 , EndNestedFraction , right parenthesis , right parenthesis , EndFraction

equals

61.9 3 3 4 1 9 2 7 0 9

Expression 14: "a" equals 9.8

Expression 15: "y" equals 6 minus sine left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis "x" left brace, "d" Subscript, "r" , Baseline cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis less than or equal to "x" less than or equal to left parenthesis, "d" Subscript, "b" , Baseline plus "d" Subscript, "r" , Baseline , right parenthesis cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , right brace

Braking distance (no antilock brakes)

Expression 17: "d" Subscript, "n" "o" "a" "n" "t" "i" "l" "o" "c" "k" , Baseline equals 1.1 5 left parenthesis, StartFraction, "v" squared Over 2 left parenthesis, "a" minus 9.8sin left parenthesis, StartNestedFraction, "s" pi NestedOver 180 , EndNestedFraction , right parenthesis , right parenthesis , EndFraction , right parenthesis

equals

71.2 2 3 4 3 2 1 6 1 6

Expression 18: "y" equals negative sine left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis "x" left brace, "d" Subscript, "r" , Baseline cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis less than or equal to "x" less than or equal to left parenthesis, "d" Subscript, "n" "o" "a" "n" "t" "i" "l" "o" "c" "k" , Baseline plus "d" Subscript, "r" , Baseline , right parenthesis cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , right brace

Expression 19: "y" equals negative sine left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis "x" left brace, 0 less than or equal to "x" less than or equal to "d" Subscript, "r" , Baseline cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , right brace

Wall

Expression 21: "x" equals left parenthesis, "d" Subscript, "b" , Baseline plus "d" Subscript, "r" , Baseline , right parenthesis cosine left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis

equals

64.3 3 1 5 1 8 7 9 7

Antilock braking systems (ABS for short) are present on most cars today, being required in every new car made since 2004. It is regarded as one of the most remarkable developments in motor vehicle history. One of the many reasons why is that it reduces braking speed on most surfaces by up to 15%. This model demonstrates how ABS can prevent a car from a potentially fatal crash by stopping before the wall.

Note to Jodi - I plan to also add an actual car on the graph, along with a time graph. Also, the graph is intentionally meant to look like a 2-lane highway.