View of /trunk/NationalProblemLibrary/Rochester/setLimitsRates1TangentVelocity/ns_2_1_5.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('tangent', 'velocity', 'average,instanteneous', 'secant line',
    3 ##'slope')
    4 ##tangent and velocity problems;
    5 ##finding average and instantenious velocities from
    6 ##the secant lines and slopes
    7 ##ENDDESCRIPTION
    8 
    9 ##KEYWORDS('Calculus')
   10 ##Tagged by ynw2d
   11 
   12 ##DBsubject('Calculus')
   13 ##DBchapter('Limits and Derivatives')
   14 ## DBsection('Tangents, Velocities, and Other Rates of Change')
   15 ## TitleText1('Calculus: Early Transcendentals')
   16 ## EditionText1('1')
   17 ## AuthorText1('Rogawski')
   18 ## Section1('2.1')
   19 ## Problem1('5')
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('1')
   22 ## AuthorText2('Rogawski')
   23 ## Section2('2.1')
   24 ## Problem2('5')
   25 
   26 DOCUMENT();        # This should be the first executable line in the problem.
   27 
   28 loadMacros ("PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl",
   29 "PGanswermacros.pl",
   30 "PGauxiliaryFunctions.pl");
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers=1;
   34 
   35 $a1=random(20, 50);
   36 $b1=random(10, 30);
   37 $init_time=random(1, 3);
   38 
   39 @times=(".01 s", ".005 s", ".002 s", ".001 s");
   40 $ans_velocity1=($a1*(.01)-$b1*(($init_time+.01)**2-($init_time)**2))/.01;
   41 $ans_velocity2=($a1*(.005)-$b1*(($init_time+.005)**2-($init_time)**2))/.005;
   42 $ans_velocity3=($a1*(.002)-$b1*(($init_time+.002)**2-($init_time)**2))/.002;
   43 $ans_velocity4=($a1*(.001)-$b1*(($init_time+.001)**2-($init_time)**2))/.001;
   44 $ans_velocity5=$a1 - 2*$b1*$init_time;
   45 
   46 TEXT(EV2(<<EOT));
   47 A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri
   48 with a velocity of
   49 $a1 ft/s.  Its height in feet after t seconds is
   50 given by \( y=${a1}t-${b1}t^{2} \). $BR $BR
   51 A.  Find the average velocity for the time period beginning
   52 when t=$init_time and lasting $BR
   53 
   54 $times[0]:\{ ans_rule(30)\} $BR
   55 $times[1]:\{ ans_rule(30)\} $BR
   56 $times[2]:\{ ans_rule(30)\} $BR
   57 $times[3]:\{ ans_rule(30)\} $BR
   58 NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. $BR
   59 EOT
   60 
   61 TEXT(EV2(
   62 "B.  Estimate the instanteneous velocity when t=$init_time. $BR"),
   63 ans_rule(10));
   64 
   65 ANS(num_cmp($ans_velocity1));
   66 ANS(num_cmp($ans_velocity2));
   67 ANS(num_cmp($ans_velocity3));
   68 ANS(num_cmp($ans_velocity4));
   69 ANS(num_cmp($ans_velocity5));
   70 
   71 ENDDOCUMENT();        # This should be the last executable line in the problem.
   72