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Sun Aug 6 16:12:44 2006 UTC (6 years, 9 months ago) by jjholt
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```Added tags.  --JH
```

```    1 ## DESCRIPTION
2 ##   Velocity and Acceleration of a Parametric Curve
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Derivative', 'Parametric', 'Path', 'Velocity', 'Acceleration')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Parametric Equations and Polar Coordinates')
10 ## DBsection('Curves Defined by Parametric Equations')
11 ## Date('')
12 ## Author('')
13 ## Institution('Union College')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "PGunion.pl",
25   "Parser.pl",
26   "parserVectorUtils.pl",
27   "PGcourse.pl"
28 );
29
30
31 TEXT(beginproblem());
32 BEGIN_PROBLEM();
33
34 ##############################################
35 #  Setup
36
37 Context("Vector")->variables->are(t=>'Real');
38
39 #
40 #  The function and derivative
41 #
42 \$a = non_zero_random(-5,5,1);
43 \$b = non_zero_random(-5,5,1);
44 \$n = random(4,7,1);
45
46 \$f = Formula("<(t + \$a)^\$n, t(1 - \$b t)>")->reduce;
47 #\$veloc = Vector("\$n(t + \$a)^".(\$n-1),"1 - ".(2*\$b)." t");
48 #\$accel = Vector((\$n*(\$n-1))."(t + \$a)^".(\$n-2),-2*\$b);
49
50 \$veloc = \$f->D('t');
51 \$accel = \$veloc->D('t');
52
53 ##############################################
54 #  Main text
55
56 \$V = Overline('v');
57 \$A = Overline('a');
58
59 Context()->texStrings;
60 BEGIN_TEXT
61
62 Consider the parametric curve \(f(t) = \$f\).
63 \$PAR
64 The velocity vector is \(\$V(t)\) = \{ans_rule(40)\}\$BR
65 and the acceleration vector is \(\$A(t)\) = \{ans_rule(40)\}.
66
67 END_TEXT
68 Context()->normalStrings;
69
70 ##################################################