Problem11

Prep Main Page > Web Conference 2 > Sample Problems > Problem 11

This is Library/Michigan/Chap2Sec1/Q17.pg

DOCUMENT();

"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGauxiliaryFunctions.pl",
"MathObjects.pl",
"parserNumberWithUnits.pl",
);

Context("Numeric");

## Do NOT show partial correct answers
$showPartialCorrectAnswers = 0; TEXT(beginproblem());$a1 = random(0.3,0.5,0.05);
$a2 = random(1.3,1.9,0.1);$b  = ($a1-0)/0.2;$c  = ($a2-$a1)/0.2;
$v = ($b+$c)/2; Context()->texStrings; BEGIN_TEXT Consider a car whose position, $$s$$, is given by the table$PAR
$BCENTER \{begintable(7) \} \{row("$$t$$ (s)" ,0,0.2,0.4,0.6,0.8,1.0) \} \{row("$$s$$ (ft)",0,$a1,$a2,3.8,6.5,9.6) \} \{endtable()\}$ECENTER

$PAR Find the average velocity over the interval $$0 \le t \le 0.2$$.$BR
average velocity = \{ ans_rule(8) \}
$PAR Estimate the velocity at $$t=0.2$$.$BR
velocity = \{ ans_rule(8) \}

END_TEXT
Context()->normalStrings;

ANS(NumberWithUnits( $b, "ft/s" )->cmp() );$bval = NumberWithUnits( $b, "ft/s" );$cval = NumberWithUnits( $c, "ft/s" );$vval = NumberWithUnits( $v, "ft/s" ); ANS(NumberWithUnits($v, "ft/s" )->cmp( checker=>sub {
my ( $correct,$student, $ansHash ) = @_; if ($student == $correct ||$student == $cval ||$student == $bval ) { return 1; } else { return 0; } } ) ); Context()->texStrings; SOLUTION(EV3(<<'END_SOLUTION'));$PAR SOLUTION $PAR The average velocity over the interval $$0 \le t \le 0.2$$ is given by$PAR
$$\frac{s(0.2)-s(0)}{0.2}=\frac{a1}{0.2}=b$$ ft/s.
$PAR The average velocity over the interval $$0.2 \le t \le 0.4$$ is given by$PAR
$$\frac{s(0.4)-s(0.2)}{0.2}=\frac{a2-a1}{0.2}=c$$ ft/s
\$PAR
A reasonable estimate for the velocity at $$t=0.2$$ is the average
$$\frac{1}{2}\cdot (b+c) = v$$ ft/s.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version');
ENDDOCUMENT();