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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 444 "Computer Intensive Phys
ics\nPhysics 211\n\nSteven R. Dunbar\nDepartment of Mathematics and St
atistics\nUniversity of Nebraska-Lincoln\nLincoln, NE, 68588\n\nsdunba
r@math.unl.edu\nhttp://www.math.unl.edu/~sdunbar\n\nTopic:  1D Dynamic
s (No/low friction with visible applied forces)\n\nTitle:  Forces that
 Vary with Time\n\nKeywords:  F=ma, Newton's Second Law, Acceleration,
 Velocity, Position\n\nAudience:  Students in Computer Lab Setting\n\n
Time:  30-45 minutes" }}{PARA 256 "" 0 "" {TEXT -1 598 "The propelling
 force (or thrust) created by an Olympic-quality sprinter in the 100-m
eter sprint event has been measured as F = 3600*exp(-k*t) (in newtons)
 where k is some positive constant.\n\nThe mass of a heavily muscled c
ompetitor such as Ben Johnson is about 90 kg.\n\nFind the constant k s
o that the sprinter can finish the 100-meter race in 10 seconds\n\nUsi
ng Newton's Second Law, you can formulate the acceleration.  Remember \+
the runner starts  with no velocity and the distance down the track is
 measured from the starting position.  This information will help you \+
set up and solve the problem\n " }}{PARA 256 "" 0 "" {TEXT -1 34 "Add \+
references to literature here." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "re
start;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "F :=3600*exp(-k*t
);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%\"FG,$-%$expG6#,$*&%\"kG\"\"\"%
\"tGF+!\"\"\"%+O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "m := 90;
" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%\"mG\"#!*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 47 "a := ;     # solve for a using your information
" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%\"aG,$-%$expG6#,$*&%\"kG\"\"\"%\"t
GF+!\"\"\"#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "v := int( ,
 t = 0..T);   # find the velocity at time T" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">%\"vG,&*&%\"kG!\"\"-%$expG6#,$*&F&\"\"\"%\"TGF-F'F-!#S*$
F&F'\"#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "s := int(  , T \+
= );    # position, watch limits of integration" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">%\"sG,&*&,&-%$expG6#,$*&%\"kG\"\"\"%#T1GF-!\"\"F-F+F-F-F
,!\"#\"#S*$F,F0!#S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s10 :
= subs( T1 = 10, s);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%$s10G,&*&,&-%$
expG6#,$%\"kG!#5\"\"\"F+\"#5F-F+!\"#\"#S*$F+F/!#S" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 22 "plot( s10, k= 1/2..5);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 29 "fsolve( s10 = 100, k, 1..10);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "$\"+'fmt*Q!\"*" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 
-1 305 "A 727 jet needs to be traveling 90 m/s to take off.  The mass \+
of the jet is 10^5 kg.  The thrust of the jet engines during take-off \+
 is 10^6*(1-exp(-t)).  The jet starts from rest.  How long must  the r
unway be?\n(Adapted from Calculus, 1st Edition, Hughes-Hallett, Gleaso
n, et.al, Problem 50, Section 6.4)" }}{PARA 256 "" 0 "" {TEXT -1 349 "
Strategy:  First we will find the acceleration from the force.  \n    \+
             Then we will find the velocity at any time.\n            \+
     Then we will find position down the runway at any time.\n        \+
         We will find out how long it takes to reach 90 m/s from the v
elocity.\n                  Then we will find the position at that tim
e. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "F :=   ;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "m :=   ;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "a :=   ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
v :=   ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "s :=   ;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fsolve(   ,    );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "subs(     ,    );" }}}}
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