When d_{b} <= 0, the car cannot stop under the selected conditions.
16
Expression 17: "d" Subscript, "b" , Baseline equals StartFraction, "v" squared Over 2 left parenthesis, "a" plus 9.8sin left parenthesis, StartNestedFraction, "s" pi NestedOver 180 , EndNestedFraction , right parenthesis , right parenthesis , EndFractiondb=v22a+9.8sinsπ180
equals=
136.1 3 7 1 2 3 9 4 6136.137123946
17
a = acceleration created when the car's brakes are pushed [m/s^2]
18
Expression 19: "a" equals 4.5a=4.5
00
2020
19
Plot the distance traveled once the brakes are pushed and the car comes to a stop with a thick red line
20
Expression 21: "y" equals "x" tangent left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis 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 bracey=xtansπ180drcossπ180≤x≤db+drcossπ180
21
Plot the position of the car with time
Hide this folder from students.
22
Expression 23: "t" equals 0t=0
00
"t" Subscript, "t" , Baselinett
23
Position of car with time before brake is pushed
24
Hidden Label: left parenthesis, "v" "t" cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , "v" "t" sin left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , right parenthesis left brace, 0 less than or equal to "t" less than or equal to "r" Subscript, "t" , Baseline , right bracevtcossπ180,vtsinsπ1800≤t≤rt
Label
equals=
left parenthesis, 0 , 0 , right parenthesis0,0
25
t_{s} = time it takes the car to stop once the brakes are pushed [s]
26
Expression 27: "t" Subscript, "s" , Baseline equals StartFraction, "v" Over 9.8sin left parenthesis, StartNestedFraction, "s" pi NestedOver 180 , EndNestedFraction , right parenthesis plus "a" , EndFractionts=v9.8sinsπ180+a
equals=
10.8 9 0 9 6 9 9 1 5 710.8909699157
27
t_{t} = total time to stop the car (reaction time + braking time) [s]
Position of car with time once the brakes are pushed
30
Hidden Label: left parenthesis, left parenthesis, "d" Subscript, "r" , Baseline plus "v" left parenthesis, "t" minus "r" Subscript, "t" , Baseline , right parenthesis minus 0.5 left parenthesis, 9.8sin left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis plus "a" , right parenthesis left parenthesis, "t" minus "r" Subscript, "t" , Baseline , right parenthesis squared , right parenthesis cos left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , left parenthesis, "d" Subscript, "r" , Baseline plus "v" left parenthesis, "t" minus "r" Subscript, "t" , Baseline , right parenthesis minus 0.5 left parenthesis, 9.8sin left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis plus "a" , right parenthesis left parenthesis, "t" minus "r" Subscript, "t" , Baseline , right parenthesis squared , right parenthesis sin left parenthesis, StartFraction, "s" pi Over 180 , EndFraction , right parenthesis , right parenthesis left brace, "r" Subscript, "t" , Baseline less than "t" less than or equal to "t" Subscript, "t" , Baseline , right bracedr+vt−rt−0.59.8sinsπ180+at−rt2cossπ180,dr+vt−rt−0.59.8sinsπ180+at−rt2sinsπ180rt<t≤tt