[npl] / trunk / NationalProblemLibrary / Rochester / setLimitsRates1TangentVelocity / ns_2_1_5.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Sat Sep 8 05:17:01 2007 UTC (5 years, 8 months ago) by sh002i
File size: 2256 byte(s)
```Added tags for Rogawski's "Calculus: Early Transcendentals".
```

```    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
30 "PGauxiliaryFunctions.pl");
31
32 TEXT(beginproblem());
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
```