Expression 11: "v" equals StartFraction, left parenthesis, "t" minus StartRoot, "t" squared minus 2abs left parenthesis, "y" Subscript, 2 , Baseline negative "y" Subscript, 1 , Baseline , right parenthesis left parenthesis, StartNestedFraction, 1 NestedOver "a" , EndNestedFraction plus StartNestedFraction, 1 NestedOver "d" , EndNestedFraction , right parenthesis , EndRoot , right parenthesis Over StartNestedFraction, 1 NestedOver "a" , EndNestedFraction plus StartNestedFraction, 1 NestedOver "d" , EndNestedFraction , EndFraction equals 0.5 2 5 3 2 7 0 8 6 3 2 9v=t−t2−2absy2−y11a+1d1a+1d
equals=
0.5 2 5 3 2 7 0 8 6 3 2 90.525327086329
11
Expression 12: "y" equals signum left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis "v" "x" plus "y" Subscript, 1 , Baseline minus signum left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis 0.5 "a" left parenthesis, StartFraction, "v" Over "a" , EndFraction , right parenthesis squared Has graph. To audio trace, press ALT+T.y=signy2−y1vx+y1−signy2−y10.5ava2
12
Acceleration Profile:
13
Expression 14: "y" equals "y" Subscript, 1 , Baseline plus signum left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis 0.5 "a" "x" squared Has graph. To audio trace, press ALT+T.y=y1+signy2−y10.5ax2
14
Deceleration Profile:
15
Expression 16: "y" equals "y" Subscript, 2 , Baseline minus signum left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis 0.5 "d" left parenthesis, "x" minus "t" , right parenthesis squared Has graph. To audio trace, press ALT+T.y=y2−signy2−y10.5dx−t2
16
Expression 17: "y" less than or equal to "y" Subscript, 1 , Baseline left brace, 0 less than or equal to "x" less than or equal to "t" , right brace left brace, "y" greater than or equal to "y" Subscript, 2 , Baseline , right brace Has graph.y≤y10≤x≤ty≥y2
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Expression 18: "y" less than or equal to "y" Subscript, 2 , Baseline left brace, 0 less than or equal to "x" less than or equal to "t" , right brace left brace, "y" greater than or equal to "y" Subscript, 1 , Baseline , right brace Has graph.y≤y20≤x≤ty≥y1