View of /trunk/rochester_problib/setDerivatives3WordProblems/s2_7_41.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('derivatives', 'velocity', 'trigonometry')
    3 ##TYPE('word problem')
    4 ##COMMENTS:
    5 ##  Find velocity and acceleration
    6 ##  of a mass attached to a string given a position
    7 ##  trigonometric function
    8 ##ENDDESCRIPTION
    9 
   10 DOCUMENT();        # This should be the first executable line in the problem.
   11 
   12 loadMacros(
   13 "PG.pl",
   14 "PGbasicmacros.pl",
   15 "PGchoicemacros.pl",
   16 "PGanswermacros.pl",
   17 "PGauxiliaryFunctions.pl"
   18 );
   19 
   20 TEXT(&beginproblem);
   21 $showPartialCorrectAnswers = 1;
   22 
   23 $a1 = random(2,5,1);
   24 $b1 = random(2,4,1);
   25 $x1 = random(1,5,1);
   26 $deriv1 = $a1 *$b1 * cos($b1*$x1);
   27 $deriv2 = -$a1 *$b1*$b1 * sin($b1*$x1);
   28 
   29 TEXT(EV2(<<EOT));
   30 A mass attached to a vertical spring has position function
   31 given by \( s(t) =  $a1 \sin ( $b1 t )  \) where \( t \) is
   32 measured in seconds and \( s \) in inches. $BR
   33 Find the velocity at time
   34 \( t= $x1 \). \{ans_rule(20) \} $BR
   35 EOT
   36 
   37 $ans = $deriv1;
   38 &ANS(std_num_cmp($ans));
   39 TEXT(EV2(<<EOT));
   40 Find the acceleration at time
   41 \( t= $x1 \). \{ans_rule(20) \}
   42 EOT
   43 
   44 $ans = $deriv2;
   45 &ANS(std_num_cmp($ans));
   46 ENDDOCUMENT();        # This should be the last executable line in the problem.