.MCAD 301010000 1 74
.CMD PLOTFORMAT
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 15
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=14 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD UNITS U=1
.TXT 3 1 0 0
Cg a73.000000,73.000000,126
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 \ul Acceleration in One
 Dimension}{ }{\f0 \fs16 by P. Fraundorf
 Copyright 1992-1995 @newton.umsl.edu: 11
 Oct 1995.}}
}
.TXT 3 0 0 0
Cg a66.125000,70.000000,96
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {First, some constants that are 
useful should you decide to change units
 in the calculation...}}
}
.TXT 3 0 0 0
Cg a10.125000,72.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {speed of light:}}
}
.EQN 0 11 0 0
c:3*(10)^(8)*(m)/(sec)
.EQN 0 12 0 0
ly:c*yr
.EQN 0 8 0 0
ly=?m
.EQN 0 16 0 0
g=?(m)/((sec)^(2))
.EQN 0 13 0 0
g=?(ly)/((yr)^(2))
.TXT 5 -60 0 0
Cg a9.250000,58.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {inertial units:}}
}
.EQN 0 10 0 0
iyr:1*yr
.EQN 0 10 0 0
c:1*(ly)/(yr)
.TXT 0 13 0 0
Cg a9.625000,28.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {traveler units:}}
}
.EQN 0 10 0 0
tyr:1*yr
.EQN 0 10 0 0
rb:1*(ly)/(yr)
.TXT 4 -53 0 0
Cg a73.000000,73.000000,417
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {There are 11 variables of interest,
 at least three of which must be specified
 in order to get the other 8.  Since there
 are 10 different combinations of those 
three initial variables within the input
 kinematic used here, we provide an index
 j=0,2*9 to be used later in summarizing
 results from any one of those 10 setup 
choices.  We initialize the variables to
 arbitrary values in defining them at this
 point...}}
}
.EQN 9 1 0 0
j:0,1;2*9
.TXT 0 11 0 0
Cg a12.125000,51.000000,20
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {distance traveled}}
}
.EQN 0 17 0 0
{0:\Dx.j}NAME:0*m
.TXT 0 16 0 0
Cg a15.500000,28.000000,24
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {constant acceleration}}
}
.EQN 0 17 0 0
(ao)[(j):0*(m)/((sec)^(2))
.TXT 3 -62 0 0
Cg a36.875000,73.000000,52
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian (Low-Velocity Approximation)
 Variables:}}
}
.TXT 3 1 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {time elapsed}}
}
.EQN 0 10 0 0
({0:\Dt}NAME)[(j):0*sec
.TXT 0 12 0 0
Cg a9.625000,50.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {initial velocity}}
}
.EQN 0 12 0 0
(vo)[(j):0*(m)/(sec)
.TXT 0 12 0 0
Cg a8.750000,26.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {final velocity}}
}
.EQN 0 12 0 0
(vf)[(j):0*(m)/(sec)
.TXT 3 -59 0 0
Cg a41.125000,73.000000,62
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Relativistic (Non-Accelerated
 Observer) Variables:}}
}
.TXT 3 1 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {time elapsed}}
}
.EQN 0 10 0 0
({0:\Db}NAME)[(j):0*iyr
.TXT 0 12 0 0
Cg a9.625000,50.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {initial velocity}}
}
.EQN 0 12 0 0
(wo)[(j):0*c
.TXT 0 12 0 0
Cg a8.750000,26.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {final velocity}}
}
.EQN 0 12 0 0
(wf)[(j):0*c
.TXT 3 -59 0 0
Cg a49.125000,73.000000,71
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler (Accelerated Observer 
or Proper-Time/4-Velocity) Variables:}}
}
.TXT 3 1 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {time elapsed}}
}
.EQN 0 10 0 0
({0:\D\t}NAME)[(j):0*tyr
.TXT 0 12 0 0
Cg a9.625000,50.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {initial velocity}}
}
.EQN 0 12 0 0
(uo)[(j):0*rb
.TXT 0 12 0 0
Cg a8.750000,26.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {final velocity}}
}
.EQN 0 12 0 0
(uf)[(j):0*rb
.TXT 5 -59 0 0
Cg a49.750000,72.000000,65
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 \ul Newtonian (or Low-Velocity
 Approximation) Inputs}}
}
.TXT 2 0 0 0
Cg a73.000000,73.000000,363
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {This worksheet assumes that }{time-related
 variables (i.e. time-elapsed and initial/final
 velocities) are specified in terms of the
 Newtonian kinematic (time parameterization).
  This time-parameterization agrees with
 physical clocks only if all velocities 
are small compared to the speed of light.
  Some useful functions }{\i given Newtonian
 inputs}{ are:  }}
}
.TXT 9 1 0 0
Cg a21.625000,72.000000,38
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\\/ }{\i relativistic energy factor}}
}
.TXT 0 52 0 0
Cg a21.125000,24.000000,37
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\\/ }{\i hyperbolic velocity angle}}
}
.EQN 4 -53 0 0
{0:\g}NAME(v):1+(1)/(2)*(((v)/(c)))^(2)
.EQN 0 18 0 0
u(v):v*\(1+(((v)/(2*c)))^(2))
.EQN 0 20 0 0
w(v):(u(v))/({0:\g}NAME(v))
.EQN 0 15 0 0
{0:\h}NAME(v):asinh((u(v))/(c))
.TXT 5 -52 0 0
Cg a9.250000,72.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Time:}}
}
.EQN 0 11 0 0
Db(ao,vf,vo,{0:\Dx}NAME,{0:\Dt}NAME):if(ao{56}0*(m)/((sec)^(2)),(u(vf)-u(vo))/(ao),if(u(vo){56}0*(m)/(sec),({0:\Dx}NAME)/(w(vo)),{0:\Dt}NAME))
.TXT 6 -11 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Proper Time:}}
}
.EQN 0 11 0 0
{0:D\t}NAME(ao,vf,vo,{0:\Dx}NAME,{0:\Dt}NAME):if(ao{56}0*(m)/((sec)^(2)),({0:\h}NAME(vf)-{0:\h}NAME(vo))/(ao)*c,if(u(vo){56}0*(m)/(sec),({0:\Dx}NAME)/(u(vo)),{0:\Dt}NAME))
.TXT 6 -12 0 0
Cg a32.250000,38.625000,81
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 0:  I}{\f0 \fs24 
\b nputs are vo, vf, and ao}{\f0 \fs24 \b 
:}}
}
.TXT 0 32 0 0
Cg a39.250000,41.250000,57
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. a rock thrown upward at 10m/s
 will go how far up?}}
}
.TXT 3 -31 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
(vo)[(0):10*(m)/(sec)
.EQN 0 22 0 0
(vf)[(0):0*(m)/(sec)
.EQN 0 21 0 0
(ao)[(0):-1*g
.TXT 3 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 3 13 0 0
({0:\Dt}NAME)[(0):((vf)[(0)-(vo)[(0))/((ao)[(0))
.EQN 0 22 0 0
({0:\Dx}NAME)[(0):(vo)[(0)*({0:\Dt}NAME)[(0)+(1)/(2)*(ao)[(0)*((({0:\Dt}NAME)[(0)))^(2)
.TXT 6 -36 0 0
Cg a32.500000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 1:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b D}{\f0 \fs24 
\b t, vo, and ao}{\f0 \fs24 \b :}}
}
.TXT 0 33 0 0
Cg a38.250000,40.000000,59
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. how far down are you 1s after
 stepping off a cliff?}}
}
.TXT 4 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dt}NAME)[(1):1*sec
.EQN 0 22 0 0
(vo)[(1):0*(m)/(sec)
.EQN 0 21 0 0
(ao)[(1):-1*g
.TXT 3 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 2 13 0 0
(vf)[(1):(vo)[(1)+(ao)[(1)*({0:\Dt}NAME)[(1)
.EQN 0 22 0 0
({0:\Dx}NAME)[(1):(vo)[(1)*({0:\Dt}NAME)[(1)+(1)/(2)*(ao)[(1)*((({0:\Dt}NAME)[(1)))^(2)
.TXT 5 -36 0 0
Cg a32.000000,38.625000,124
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 2:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b t, vf, and ao}{\f0 \fs24 
\b :}}
}
.TXT 0 33 0 0
Cg a40.000000,40.000000,55
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. what speed is needed to travel
 up for 1 second?}}
}
.TXT 3 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dt}NAME)[(2):1*sec
.EQN 0 22 0 0
(vf)[(2):0*(m)/(sec)
.EQN 0 21 0 0
(ao)[(2):-1*g
.TXT 4 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 1 14 0 0
(vo)[(2):(vf)[(2)-(ao)[(2)*({0:\Dt}NAME)[(2)
.EQN 0 22 0 0
({0:\Dx}NAME)[(2):(vo)[(2)*({0:\Dt}NAME)[(2)+(1)/(2)*(ao)[(2)*((({0:\Dt}NAME)[(2)))^(2)
.TXT 4 -37 0 0
C x1,1,0,0
.TXT 6 0 0 0
Cg a32.000000,38.625000,124
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 3:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b t, vo, and vf}{\f0 \fs24 
\b :}}
}
.TXT 0 33 0 0
Cg a37.750000,39.000000,55
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. 0 to 60 mph in 6 sec implies
 what acceleration?}}
}
.TXT 4 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dt}NAME)[(3):6*sec
.EQN 0 22 0 0
(vo)[(3):0*(mi)/(hr)
.EQN 0 21 0 0
(vf)[(3):60*(mi)/(hr)
.TXT 3 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 3 14 0 0
(ao)[(3):((vf)[(3)-(vo)[(3))/(({0:\Dt}NAME)[(3))
.EQN 0 20 0 0
({0:\Dx}NAME)[(3):(vo)[(3)*({0:\Dt}NAME)[(3)+(1)/(2)*(ao)[(3)*((({0:\Dt}NAME)[(3)))^(2)
.TXT 5 -35 0 0
Cg a32.875000,38.625000,124
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 4:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b x, vo, and ao}{\f0 \fs24 
\b :}}
}
.TXT 0 34 0 0
Cg a36.125000,38.000000,53
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. time for a 1-g space dragster
 in a 4-ly race?}}
}
.TXT 4 -33 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dx}NAME)[(4):4*ly
.EQN 0 22 0 0
(vo)[(4):0*(m)/(sec)
.EQN 0 21 0 0
(ao)[(4):1*g
.TXT 3 -49 0 0
Cg a11.250000,72.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then EITHER...}}
}
.EQN 3 14 0 0
(vf)[(4):\((((vo)[(4)))^(2)+2*(ao)[(4)*({0:\Dx}NAME)[(4))
.EQN 0 25 0 0
({0:\Dt}NAME)[(4):((vf)[(4)-(vo)[(4))/((ao)[(4))
.TXT 3 -35 0 0
Cg a3.875000,70.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {OR...}}
}
.EQN 3 10 0 0
(vf)[(14):-\((((vo)[(4)))^(2)+2*(ao)[(4)*({0:\Dx}NAME)[(4))
.EQN 0 25 0 0
({0:\Dt}NAME)[(14):((vf)[(14)-(vo)[(4))/((ao)[(4))
.TXT 5 -40 0 0
Cg a32.375000,38.625000,124
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 5:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b x, vf, and ao}{\f0 \fs24 
\b :}}
}
.TXT 0 33 0 0
Cg a34.625000,40.000000,54
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. how long for a fly ball to
 peak at 80 feet up?}}
}
.TXT 3 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dx}NAME)[(5):80*ft
.EQN 0 22 0 0
(vf)[(5):0*(m)/(sec)
.EQN 0 21 0 0
(ao)[(5):-1*g
.TXT 4 -49 0 0
Cg a11.250000,72.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then EITHER...}}
}
.EQN 2 14 0 0
(vo)[(5):\((((vf)[(5)))^(2)-2*(ao)[(5)*({0:\Dx}NAME)[(5))
.EQN 0 25 0 0
({0:\Dt}NAME)[(5):((vf)[(5)-(vo)[(5))/((ao)[(5))
.TXT 4 -35 0 0
Cg a3.875000,70.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
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{\plain {OR...}}
}
.EQN 2 10 0 0
(vo)[(15):-\((((vf)[(5)))^(2)-2*(ao)[(5)*({0:\Dx}NAME)[(5))
.EQN 0 25 0 0
({0:\Dt}NAME)[(15):((vf)[(5)-(vo)[(15))/((ao)[(5))
.TXT 5 -40 0 0
Cg a32.375000,38.625000,124
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 6:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b x, vo, and vf}{\f0 \fs24 
\b :}}
}
.TXT 0 33 0 0
Cg a40.000000,40.000000,56
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. deceleration needed for a 
300ft stop from 70mph?}}
}
.TXT 3 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 8 0 0
({0:\Dx}NAME)[(6):300*ft
.EQN 0 20 0 0
(vo)[(6):70*(mi)/(hr)
.EQN 0 20 0 0
(vf)[(6):0*(mi)/(hr)
.TXT 5 -48 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 1 14 0 0
(ao)[(6):((((vf)[(6)))^(2)-(((vo)[(6)))^(2))/(2*({0:\Dx}NAME)[(6))
.EQN 0 24 0 0
({0:\Dt}NAME)[(6):((vf)[(6)-(vo)[(6))/((ao)[(6))
.TXT 5 -39 0 0
Cg a32.875000,38.625000,167
{\rtf1\ansi \deff0
{\fonttbl
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{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 7:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b t, }{\f0 \fs24 \b \f1 \fs24 
\b D}{\f0 \fs24 \b x, and ao}{\f0 \fs24 
\b :}}
}
.TXT 0 33 0 0
Cg a38.875000,40.000000,56
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. upward speed to travel 10 
miles up in 5 seconds?}}
}
.TXT 4 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dt}NAME)[(7):5*sec
.EQN 0 22 0 0
({0:\Dx}NAME)[(7):10*mi
.EQN 0 21 0 0
(ao)[(7):-1*g
.TXT 3 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 3 12 0 0
(vo)[(7):(({0:\Dx}NAME)[(7))/(({0:\Dt}NAME)[(7))-((ao)[(7)*({0:\Dt}NAME)[(7))/(2)
.EQN 0 25 0 0
(vf)[(7):(({0:\Dx}NAME)[(7))/(({0:\Dt}NAME)[(7))+((ao)[(7)*({0:\Dt}NAME)[(7))/(2)
.TXT 6 -38 0 0
Cg a32.875000,38.625000,167
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 8:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b t, }{\f0 \fs24 \b \f1 \fs24 
\b D}{\f0 \fs24 \b x, and vo}{\f0 \fs24 
\b :}}
}
.TXT 0 33 0 0
Cg a38.875000,39.000000,58
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. final speed in a 10 second
 quarter mile from rest?}}
}
.TXT 4 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dt}NAME)[(8):10*sec
.EQN 0 22 0 0
({0:\Dx}NAME)[(8):0.25*mi
.EQN 0 21 0 0
(vo)[(8):0*(mi)/(hr)
.TXT 3 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 3 11 0 0
(ao)[(8):(2*(({0:\Dx}NAME)[(8)-(vo)[(8)*({0:\Dt}NAME)[(8)))/(((({0:\Dt}NAME)[(8)))^(2))
.EQN 0 26 0 0
(vf)[(8):(vo)[(8)+(ao)[(8)*({0:\Dt}NAME)[(8)
.TXT 6 -38 0 0
Cg a33.500000,38.625000,167
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 9:  I}{\f0 \fs24 
\b nputs are }{\f0 \fs24 \b \f1 \fs24 \b 
D}{\f0 \fs24 \b t, }{\f0 \fs24 \b \f1 \fs24 
\b D}{\f0 \fs24 \b x, and vf}{\f0 \fs24 
\b :}}
}
.TXT 0 34 0 0
Cg a36.375000,39.000000,53
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. speed going into a 2 sec, 
30 meter skid stop?}}
}
.TXT 4 -33 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dt}NAME)[(9):2*sec
.EQN 0 22 0 0
({0:\Dx}NAME)[(9):30*m
.EQN 0 21 0 0
(vf)[(9):0*(m)/(sec)
.TXT 3 -49 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 3 12 0 0
(ao)[(9):(-2*(({0:\Dx}NAME)[(9)-(vf)[(9)*({0:\Dt}NAME)[(9)))/(((({0:\Dt}NAME)[(9)))^(2))
.EQN 0 25 0 0
(vo)[(9):(vf)[(9)-(ao)[(9)*({0:\Dt}NAME)[(9)
.TXT 5 -38 0 0
C x1,1,0,0
.TXT 8 0 0 0
Cg a43.875000,73.000000,72
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\ul \f0 \fs28 \b Results Report
 From Newtonian Inputs}{\f0 \fs28 \b :}}
}
.TXT 0 48 0 0
Cg a14.500000,71.000000,22
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\i For Case Number:}}
}
.EQN 0 16 0 0
i:4
.TXT 4 -63 0 0
Cg a66.750000,72.000000,77
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Variables which are Independent
 of Kinematic or Time-Parameterization are:}}
}
.TXT 3 2 0 0
Cg a6.875000,68.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Distance:}}
}
.EQN 0 8 0 0
({0:\Dx}NAME)[(i)=?m
.TXT 0 17 0 0
Cg a16.500000,47.000000,25
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Constant Acceleration:}}
}
.EQN 0 17 0 0
(ao)[(i)=?g
.TXT 4 -44 0 0
Cg a47.625000,72.000000,66
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian (Low-Velocity Approximation)
 Velocities/Elapsed-Time:}}
}
.EQN 4 0 0 0
(vo)[(i)=?(m)/(sec)
.EQN 0 22 0 0
(vf)[(i)=?(m)/(sec)
.EQN 0 22 0 0
({0:\Dt}NAME)[(i)=?sec
.TXT 4 -44 0 0
Cg a51.875000,72.000000,76
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Relativistic (Non-Accelerated
 Observer) Velocities/Elapsed-Time:}}
}
.EQN 3 0 0 0
(wo)[(i):w((vo)[(i))
.EQN 0 22 0 0
(wf)[(i):w((vf)[(i))
.EQN 0 22 0 0
({0:\Db}NAME)[(i):Db((ao)[(i),(vf)[(i),(vo)[(i),({0:\Dx}NAME)[(i),({0:\Dt}NAME)[(i))
.EQN 3 -44 0 0
(wo)[(i)=?c
.EQN 0 22 0 0
(wf)[(i)=?c
.EQN 0 22 0 0
({0:\Db}NAME)[(i)=?iyr
.TXT 3 -44 0 0
Cg a71.750000,72.000000,79
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler (Accelerated Observer)
 Vector 4-Velocities and Elapsed Proper-Time:}}
}
.EQN 3 0 0 0
(uo)[(i):u((vo)[(i))
.EQN 0 22 0 0
(uf)[(i):u((vf)[(i))
.EQN 0 22 0 0
({0:\D\t}NAME)[(i):{0:D\t}NAME((ao)[(i),(vf)[(i),(vo)[(i),({0:\Dx}NAME)[(i),({0:\Dt}NAME)[(i))
.EQN 3 -44 0 0
(uo)[(i)=?rb
.EQN 0 22 0 0
(uf)[(i)=?rb
.EQN 0 22 0 0
({0:\D\t}NAME)[(i)=?tyr
.TXT 7 -45 0 0
Cg a27.875000,73.000000,39
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 Some Graphs of the Result:}}
}
.EQN 6 20 0 0
vT(t):(vo)[(i)+(ao)[(i)*t
.EQN 0 18 0 0
x(t):(vo)[(i)*t+(1)/(2)*(ao)[(i)*(t)^(2)
.TXT 0 16 0 0
Cg a16.625000,18.375000,117
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {= }{\f0 \fs24 (}{\f1 \fs20 g[}{vT(t)]-}{\f1 
\fs20 g}{[vo}{\dn6 i}{]}{\f0 \fs24 ) }{c}{\f0 
\fs16 \up6 2}{/ao}{\dn6 i}}
}
.EQN 5 -34 0 0
wT(t):w(vT(t))
.EQN 0 18 0 0
b(t):Db((ao)[(i),vT(t),(vo)[(i),x(t),t)
.EQN 4 -17 0 0
uT(t):u(vT(t))
.EQN 0 17 0 0
{0:\t}NAME(t):{0:D\t}NAME((ao)[(i),vT(t),(vo)[(i),x(t),t)
.EQN 5 -12 0 0
tInc:(({0:\Dt}NAME)[(i))/(100)
.EQN 0 12 0 0
t:0*sec,tInc;({0:\Dt}NAME)[(i)
.EQN 4 -38 0 0
&&b(t),t,{0:\t}NAME(t)@&&x(t)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 23 17
.EQN 0 37 0 0
&&wT(t),vT(t),uT(t)@&&x(t)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 22 17
.EQN 23 -37 0 0
&&b(t),t,{0:\t}NAME(t)@&&t
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 23 17
.EQN 1 37 0 0
&&wT(t),vT(t),uT(t)@&&t
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 22 17
.TXT 25 -37 0 0
C x1,1,0,0
.TXT 5 1 0 0
Cg a71.500000,72.000000,95
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {For Cases with i=4,5, a Set of 
Different Kinematic-Dependent Values may
 also Fit the Inputs:}}
}
.TXT 5 3 0 0
Cg a31.750000,69.000000,48
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {We first set up the Alternative
 Value Arrays:}}
}
.EQN 0 39 0 0
k:0,1;9
.EQN 3 -43 0 0
(vo)[(k+10):if(k÷5,(vo)[(k+10),(vo)[(k))
.EQN 0 22 0 0
(vf)[(k+10):if(k÷4,(vf)[(k+10),(vf)[(k))
.EQN 0 21 0 0
({0:\Dt}NAME)[(k+10):if(k<4,({0:\Dt}NAME)[(k),if(k>6,({0:\Dt}NAME)[(k),({0:\Dt}NAME)[(k+10)))
.TXT 5 -39 0 0
Cg a31.500000,71.000000,48
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {The Alternative Value Index for
 this Case is:}}
}
.EQN 0 33 0 0
k:i+10
.TXT 0 10 0 0
Cg a17.375000,26.000000,26
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {which has Values for...}}
}
.TXT 3 -46 0 0
Cg a47.625000,72.000000,66
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian (Low-Velocity Approximation)
 Velocities/Elapsed-Time:}}
}
.EQN 4 0 0 0
(vo)[(k)=?(m)/(sec)
.EQN 0 22 0 0
(vf)[(k)=?(m)/(sec)
.EQN 0 22 0 0
({0:\Dt}NAME)[(k)=?sec
.TXT 4 -44 0 0
Cg a51.875000,72.000000,76
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Relativistic (Non-Accelerated
 Observer) Velocities/Elapsed-Time:}}
}
.EQN 3 0 0 0
(wo)[(k):w((vo)[(k))
.EQN 0 22 0 0
(wf)[(k):w((vf)[(k))
.EQN 0 22 0 0
({0:\Db}NAME)[(k):Db((ao)[(i),(vf)[(k),(vo)[(k),({0:\Dx}NAME)[(i),({0:\Dt}NAME)[(k))
.EQN 3 -44 0 0
(wo)[(k)=?c
.EQN 0 22 0 0
(wf)[(k)=?c
.EQN 0 22 0 0
({0:\Db}NAME)[(k)=?iyr
.TXT 3 -44 0 0
Cg a71.750000,72.000000,79
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler (Accelerated Observer)
 Vector 4-Velocities and Elapsed Proper-Time:}}
}
.EQN 3 0 0 0
(uo)[(k):u((vo)[(k))
.EQN 0 22 0 0
(uf)[(k):u((vf)[(k))
.EQN 0 22 0 0
({0:\D\t}NAME)[(k):{0:D\t}NAME((ao)[(i),(vf)[(k),(vo)[(k),({0:\Dx}NAME)[(i),({0:\Dt}NAME)[(k))
.EQN 3 -44 0 0
(uo)[(k)=?rb
.EQN 0 22 0 0
(uf)[(k)=?rb
.EQN 0 22 0 0
({0:\D\t}NAME)[(k)=?tyr
.TXT 6 -45 0 0
Cg a27.875000,73.000000,39
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 Some Graphs of the Result:}}
}
.EQN 5 20 0 0
vT(t):(vo)[(k)+(ao)[(i)*t
.EQN 0 18 0 0
x(t):(vo)[(k)*t+(1)/(2)*(ao)[(i)*(t)^(2)
.TXT 0 16 0 0
Cg a16.625000,18.375000,117
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {= }{\f0 \fs24 (}{\f1 \fs20 g[}{vT(t)]-}{\f1 
\fs20 g}{[vo}{\dn6 i}{]}{\f0 \fs24 ) }{c}{\f0 
\fs16 \up6 2}{/ao}{\dn6 i}}
}
.EQN 5 -34 0 0
wT(t):w(vT(t))
.EQN 0 18 0 0
b(t):Db((ao)[(i),vT(t),(vo)[(k),x(t),t)
.EQN 4 -18 0 0
uT(t):u(vT(t))
.EQN 0 18 0 0
{0:\t}NAME(t):{0:D\t}NAME((ao)[(i),vT(t),(vo)[(k),x(t),t)
.EQN 6 -13 0 0
tinc:(({0:\Dt}NAME)[(k))/(100)
.EQN 0 13 0 0
t:0*sec,tinc;({0:\Dt}NAME)[(k)
.EQN 5 -38 0 0
&&b(t),t,{0:\t}NAME(t)@&&x(t)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 15
.EQN 0 39 0 0
&&wT(t),vT(t),uT(t)@&&x(t)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 15
.EQN 22 -39 0 0
&&b(t),t,{0:\t}NAME(t)@&&t
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 20 17
.EQN 0 38 0 0
&&wT(t),vT(t),uT(t)@&&t
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 17