Gezmat http://gezmat.com

Test for eager students, for your holiday
Warszawa, 2017-09-09
\emph{ It could be prepared by a teacher of your \textbf{favourite} subject... }
Write your solution of each problem on a separate, signed sheet Clearly indicate the problem number. Please, let us know if you find a b\underline{a}g in \textsc{Gezmat}... ;-)
----------------------------------------------------------

In the following number snake a number in each box except the first one must be equal to the number from the previous box modified in accordance with the description at the arrow. Enter the appropriate numbers in the empty boxes.

\begin{center}
\begin{asy}[width=0.95\textwidth, height=0.85\textheight, keepAspect=true]

import flowchart;

unitsize(1bp); // Very important. With size() or other values width of the pen scales differently than sizes of objects.

defaultpen(fontsize( 24pt )+linewidth( 1.000000 ));

real l = 50.000000; // Length unit

int numberOfBlocksInRow = 3;

string numbers[] = {"$1$", "$1$", "$5$", "$6$"};
string modifiers[] = {"\boldmath$+0$", "\boldmath$+4$", "\boldmath$+1$"};

int n = numbers.length;

block blocks[];

real x[] = {0.000000, 47.815000, 102.155000, 58.822000};
real y[] = {0.000000, -3.430000, -6.512500, -38.317500};
for (int i = 0; i < n; ++i) {if (i < 1) {
blocks[i] = roundrectangle("\boldmath"+numbers[i], (x[i], y[i]));
}
else {
blocks[i] = roundrectangle("\phantom{"+"\boldmath"+numbers[i]+"}", (x[i], y[i]));
}
draw(blocks[i]);
}

add(new void(picture pic, transform t) {
blockconnector operator --=blockconnector(pic,t);
bool toRight = true;
for (int i = 0; i < n - 1; ++i) {
if ((i + 1) % numberOfBlocksInRow != 0) { // In on row
if (toRight) {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].right(t){E}..{E}blocks[i+1].left(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].left(t){W}..{W}blocks[i+1].right(t), Arrow);
}
}
else {
if (i < n - 1) { // Next row starts
if (toRight) {
draw(pic,Label(modifiers[i],0.5,NW),blocks[i].bottom(t){S}..{W}blocks[i+1].right(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,NE),blocks[i].bottom(t){S}..{E}blocks[i+1].left(t), Arrow);
}
}
toRight = ! toRight;
}
}
});

\end{asy}
\end{center}

\begin{center}
\begin{asy}[width=0.95\textwidth, height=0.85\textheight, keepAspect=true]

import flowchart;

unitsize(1bp); // Very important. With size() or other values width of the pen scales differently than sizes of objects.

defaultpen(fontsize( 24pt )+linewidth( 1.000000 ));

real l = 50.000000; // Length unit

int numberOfBlocksInRow = 3;

string numbers[] = {"$1$", "$1$", "$5$", "$6$"};
string modifiers[] = {"\boldmath$+0$", "\boldmath$+4$", "\boldmath$+1$"};

int n = numbers.length;

block blocks[];

real x[] = {0.000000, 47.815000, 102.155000, 58.822000};
real y[] = {0.000000, -3.430000, -6.512500, -38.317500};
for (int i = 0; i < n; ++i) {if (i < n) {
blocks[i] = roundrectangle("\boldmath"+numbers[i], (x[i], y[i]));
}
else {
blocks[i] = roundrectangle("\phantom{"+"\boldmath"+numbers[i]+"}", (x[i], y[i]));
}
draw(blocks[i]);
}

add(new void(picture pic, transform t) {
blockconnector operator --=blockconnector(pic,t);
bool toRight = true;
for (int i = 0; i < n - 1; ++i) {
if ((i + 1) % numberOfBlocksInRow != 0) { // In on row
if (toRight) {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].right(t){E}..{E}blocks[i+1].left(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].left(t){W}..{W}blocks[i+1].right(t), Arrow);
}
}
else {
if (i < n - 1) { // Next row starts
if (toRight) {
draw(pic,Label(modifiers[i],0.5,NW),blocks[i].bottom(t){S}..{W}blocks[i+1].right(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,NE),blocks[i].bottom(t){S}..{E}blocks[i+1].left(t), Arrow);
}
}
toRight = ! toRight;
}
}
});

\end{asy}
\end{center}

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Number snake, subtraction of multiples of 10, 0--100

In the following number snake a number in each box except the first one must be equal to the number from the previous box modified in accordance with the description at the arrow. Enter the appropriate numbers in the empty boxes.

\begin{center}
\begin{asy}[width=0.95\textwidth, height=0.85\textheight, keepAspect=true]

import flowchart;

unitsize(1bp); // Very important. With size() or other values width of the pen scales differently than sizes of objects.

defaultpen(fontsize( 24pt )+linewidth( 1.000000 ));

real l = 50.000000; // Length unit

int numberOfBlocksInRow = 3;

string numbers[] = {"$90$", "$60$", "$60$", "$60$", "$40$", "$20$"};
string modifiers[] = {"\boldmath$-30$", "\boldmath$-0$", "\boldmath$-0$", "\boldmath$-20$", "\boldmath$-20$"};

int n = numbers.length;

block blocks[];

real x[] = {0.000000, 41.860000, 86.675000, 51.604000, 4.614000, -43.651000};
real y[] = {0.000000, -3.195000, -7.812500, -38.272500, -42.847500, -46.222500};
for (int i = 0; i < n; ++i) {if (i < 1) {
blocks[i] = roundrectangle("\boldmath"+numbers[i], (x[i], y[i]));
}
else {
blocks[i] = roundrectangle("\phantom{"+"\boldmath"+numbers[i]+"}", (x[i], y[i]));
}
draw(blocks[i]);
}

add(new void(picture pic, transform t) {
blockconnector operator --=blockconnector(pic,t);
bool toRight = true;
for (int i = 0; i < n - 1; ++i) {
if ((i + 1) % numberOfBlocksInRow != 0) { // In on row
if (toRight) {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].right(t){E}..{E}blocks[i+1].left(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].left(t){W}..{W}blocks[i+1].right(t), Arrow);
}
}
else {
if (i < n - 1) { // Next row starts
if (toRight) {
draw(pic,Label(modifiers[i],0.5,NW),blocks[i].bottom(t){S}..{W}blocks[i+1].right(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,NE),blocks[i].bottom(t){S}..{E}blocks[i+1].left(t), Arrow);
}
}
toRight = ! toRight;
}
}
});

\end{asy}
\end{center}

\begin{center}
\begin{asy}[width=0.95\textwidth, height=0.85\textheight, keepAspect=true]

import flowchart;

unitsize(1bp); // Very important. With size() or other values width of the pen scales differently than sizes of objects.

defaultpen(fontsize( 24pt )+linewidth( 1.000000 ));

real l = 50.000000; // Length unit

int numberOfBlocksInRow = 3;

string numbers[] = {"$90$", "$60$", "$60$", "$60$", "$40$", "$20$"};
string modifiers[] = {"\boldmath$-30$", "\boldmath$-0$", "\boldmath$-0$", "\boldmath$-20$", "\boldmath$-20$"};

int n = numbers.length;

block blocks[];

real x[] = {0.000000, 41.860000, 86.675000, 51.604000, 4.614000, -43.651000};
real y[] = {0.000000, -3.195000, -7.812500, -38.272500, -42.847500, -46.222500};
for (int i = 0; i < n; ++i) {if (i < n) {
blocks[i] = roundrectangle("\boldmath"+numbers[i], (x[i], y[i]));
}
else {
blocks[i] = roundrectangle("\phantom{"+"\boldmath"+numbers[i]+"}", (x[i], y[i]));
}
draw(blocks[i]);
}

add(new void(picture pic, transform t) {
blockconnector operator --=blockconnector(pic,t);
bool toRight = true;
for (int i = 0; i < n - 1; ++i) {
if ((i + 1) % numberOfBlocksInRow != 0) { // In on row
if (toRight) {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].right(t){E}..{E}blocks[i+1].left(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].left(t){W}..{W}blocks[i+1].right(t), Arrow);
}
}
else {
if (i < n - 1) { // Next row starts
if (toRight) {
draw(pic,Label(modifiers[i],0.5,NW),blocks[i].bottom(t){S}..{W}blocks[i+1].right(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,NE),blocks[i].bottom(t){S}..{E}blocks[i+1].left(t), Arrow);
}
}
toRight = ! toRight;
}
}
});

\end{asy}
\end{center}

----------------------------------------------------------
~\newline
Number snake, subtraction of multiples of 10, 0--100

In the following number snake a number in each box except the first one must be equal to the number from the previous box modified in accordance with the description at the arrow. Enter the appropriate numbers in the empty boxes.

\begin{center}
\begin{asy}[width=0.95\textwidth, height=0.85\textheight, keepAspect=true]

import flowchart;

unitsize(1bp); // Very important. With size() or other values width of the pen scales differently than sizes of objects.

defaultpen(fontsize( 24pt )+linewidth( 1.000000 ));

real l = 50.000000; // Length unit

int numberOfBlocksInRow = 3;

string numbers[] = {"$80$", "$50$", "$20$"};
string modifiers[] = {"\boldmath$-30$", "\boldmath$-30$"};

int n = numbers.length;

block blocks[];

real x[] = {0.000000, 53.380000, 96.725000};
real y[] = {0.000000, -3.117500, -6.175000};
for (int i = 0; i < n; ++i) {if (i < 1) {
blocks[i] = roundrectangle("\boldmath"+numbers[i], (x[i], y[i]));
}
else {
blocks[i] = roundrectangle("\phantom{"+"\boldmath"+numbers[i]+"}", (x[i], y[i]));
}
draw(blocks[i]);
}

add(new void(picture pic, transform t) {
blockconnector operator --=blockconnector(pic,t);
bool toRight = true;
for (int i = 0; i < n - 1; ++i) {
if ((i + 1) % numberOfBlocksInRow != 0) { // In on row
if (toRight) {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].right(t){E}..{E}blocks[i+1].left(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].left(t){W}..{W}blocks[i+1].right(t), Arrow);
}
}
else {
if (i < n - 1) { // Next row starts
if (toRight) {
draw(pic,Label(modifiers[i],0.5,NW),blocks[i].bottom(t){S}..{W}blocks[i+1].right(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,NE),blocks[i].bottom(t){S}..{E}blocks[i+1].left(t), Arrow);
}
}
toRight = ! toRight;
}
}
});

\end{asy}
\end{center}

~\\ \begin{center} {\bf From the following 8 problems 2 are randomly chosen.} \end{center}

\begin{center}
\begin{asy}[width=0.95\textwidth, height=0.85\textheight, keepAspect=true]

import flowchart;

unitsize(1bp); // Very important. With size() or other values width of the pen scales differently than sizes of objects.

defaultpen(fontsize( 24pt )+linewidth( 1.000000 ));

real l = 50.000000; // Length unit

int numberOfBlocksInRow = 3;

string numbers[] = {"$80$", "$50$", "$20$"};
string modifiers[] = {"\boldmath$-30$", "\boldmath$-30$"};

int n = numbers.length;

block blocks[];

real x[] = {0.000000, 53.380000, 96.725000};
real y[] = {0.000000, -3.117500, -6.175000};
for (int i = 0; i < n; ++i) {if (i < n) {
blocks[i] = roundrectangle("\boldmath"+numbers[i], (x[i], y[i]));
}
else {
blocks[i] = roundrectangle("\phantom{"+"\boldmath"+numbers[i]+"}", (x[i], y[i]));
}
draw(blocks[i]);
}

add(new void(picture pic, transform t) {
blockconnector operator --=blockconnector(pic,t);
bool toRight = true;
for (int i = 0; i < n - 1; ++i) {
if ((i + 1) % numberOfBlocksInRow != 0) { // In on row
if (toRight) {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].right(t){E}..{E}blocks[i+1].left(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,1.1N),blocks[i].left(t){W}..{W}blocks[i+1].right(t), Arrow);
}
}
else {
if (i < n - 1) { // Next row starts
if (toRight) {
draw(pic,Label(modifiers[i],0.5,NW),blocks[i].bottom(t){S}..{W}blocks[i+1].right(t), Arrow);
}
else {
draw(pic,Label(modifiers[i],0.5,NE),blocks[i].bottom(t){S}..{E}blocks[i+1].left(t), Arrow);
}
}
toRight = ! toRight;
}
}
});

\end{asy}
\end{center}

----------------------------------------------------------

In the following number triangle in each rectangle except those in the lowest row there must be a number that is the sum of the numbers from the two nearest rectangles from the lower row. Enter the appropriate numbers in the empty rectangles.\begin{center}
{\huge \bf

\renewcommand{\arraystretch}{1.2}
\begin{tabular}{ *{8}{m{5mm}} }
\cline{4-5}
~ &  ~ &  ~ & \multicolumn{2}{|c|}{ ~ } & ~  & ~  & ~ \\
\cline{3-6}
~ &  ~ & \multicolumn{2}{|c}{ ~ } & \multicolumn{2}{|c|}{ ~ } & ~  & ~ \\
\cline{2-7}
~ & \multicolumn{2}{|c}{$5$} & \multicolumn{2}{|c}{ ~ } & \multicolumn{2}{|c|}{$4$} & ~ \\
\cline{1-8}
\multicolumn{2}{|c}{$1$} & \multicolumn{2}{|c}{ ~ } & \multicolumn{2}{|c}{$1$} & \multicolumn{2}{|c|}{ ~ }\\
\hline
~ & ~ &  ~ & ~ &  ~ & ~ &  ~ & ~ \\[-3ex] % multicolumn cannot be in this row. There must be some row without multicolumn.
\end{tabular}
} \end{center}

~\\ \begin{center} {\bf All gzm commands work in from-group-choose} \end{center}

\begin{center}
{\huge \bf

\renewcommand{\arraystretch}{1.2}
\begin{tabular}{ *{8}{m{5mm}} }
\cline{4-5}
~ &  ~ &  ~ & \multicolumn{2}{|c|}{$19$} & ~  & ~  & ~ \\
\cline{3-6}
~ &  ~ & \multicolumn{2}{|c}{$10$} & \multicolumn{2}{|c|}{$9$} & ~  & ~ \\
\cline{2-7}
~ & \multicolumn{2}{|c}{$5$} & \multicolumn{2}{|c}{$5$} & \multicolumn{2}{|c|}{$4$} & ~ \\
\cline{1-8}
\multicolumn{2}{|c}{$1$} & \multicolumn{2}{|c}{$4$} & \multicolumn{2}{|c}{$1$} & \multicolumn{2}{|c|}{$3$}\\
\hline
~ & ~ &  ~ & ~ &  ~ & ~ &  ~ & ~ \\[-3ex] % multicolumn cannot be in this row. There must be some row without multicolumn.
\end{tabular}
} \end{center}

----------------------------------------------------------
Number triangle, subtraction, 0--20

In the following number triangle in each rectangle except those in the lowest row there must be a number that is the difference of the numbers from the two nearest rectangles from the lower row: from the number in the left rectangle the number in the right rectangle is subtracted. Enter the appropriate numbers in the empty rectangles.\begin{center}
{\huge \bf

\renewcommand{\arraystretch}{1.2}
\begin{tabular}{ *{8}{m{5mm}} }
\cline{4-5}
~ &  ~ &  ~ & \multicolumn{2}{|c|}{ ~ } & ~  & ~  & ~ \\
\cline{3-6}
~ &  ~ & \multicolumn{2}{|c}{ ~ } & \multicolumn{2}{|c|}{ ~ } & ~  & ~ \\
\cline{2-7}
~ & \multicolumn{2}{|c}{ ~ } & \multicolumn{2}{|c}{ ~ } & \multicolumn{2}{|c|}{ ~ } & ~ \\
\cline{1-8}
\multicolumn{2}{|c}{$19$} & \multicolumn{2}{|c}{$10$} & \multicolumn{2}{|c}{$10$} & \multicolumn{2}{|c|}{$10$}\\
\hline
~ & ~ &  ~ & ~ &  ~ & ~ &  ~ & ~ \\[-3ex] % multicolumn cannot be in this row. There must be some row without multicolumn.
\end{tabular}
} \end{center}

\begin{center}
{\huge \bf

\renewcommand{\arraystretch}{1.2}
\begin{tabular}{ *{8}{m{5mm}} }
\cline{4-5}
~ &  ~ &  ~ & \multicolumn{2}{|c|}{$9$} & ~  & ~  & ~ \\
\cline{3-6}
~ &  ~ & \multicolumn{2}{|c}{$9$} & \multicolumn{2}{|c|}{$0$} & ~  & ~ \\
\cline{2-7}
~ & \multicolumn{2}{|c}{$9$} & \multicolumn{2}{|c}{$0$} & \multicolumn{2}{|c|}{$0$} & ~ \\
\cline{1-8}
\multicolumn{2}{|c}{$19$} & \multicolumn{2}{|c}{$10$} & \multicolumn{2}{|c}{$10$} & \multicolumn{2}{|c|}{$10$}\\
\hline
~ & ~ &  ~ & ~ &  ~ & ~ &  ~ & ~ \\[-3ex] % multicolumn cannot be in this row. There must be some row without multicolumn.
\end{tabular}
} \end{center}

----------------------------------------------------------

Calculate the following sums. \\[3ex] \begin{minipage}{.495\textwidth} \begin{center}
a)~~~~{\huge
${ \renewcommand{\arraystretch}{1.2} \setlength{\arrayrulewidth}{3\arrayrulewidth} \begin{tabu}{*{3}{|c}|} \taburulecolor{gray!60} \hline \phantom{88} & \phantom{88} & \phantom{88} \tabularnewline \hline \phantom{88} & 5 & 3 \tabularnewline \hline + & 3 & 4 \tabularnewline \tabucline[1.2\arrayrulewidth black]{-} \phantom{88} & \phantom{88} & \phantom{88} \tabularnewline \hline \end{tabu} }$
} \end{center} \end{minipage}\begin{minipage}{.495\textwidth} \begin{center}
b)~~~~{\huge
${ \renewcommand{\arraystretch}{1.2} \setlength{\arrayrulewidth}{3\arrayrulewidth} \begin{tabu}{*{3}{|c}|} \taburulecolor{gray!60} \hline \phantom{88} & \phantom{88} & \phantom{88} \tabularnewline \hline \phantom{88} & 6 & 3 \tabularnewline \hline + & 3 & 6 \tabularnewline \tabucline[1.2\arrayrulewidth black]{-} \phantom{88} & \phantom{88} & \phantom{88} \tabularnewline \hline \end{tabu} }$
} \end{center} \end{minipage}

\begin{minipage}{.495\textwidth} \begin{center}
a)~~~~{\huge
${ \renewcommand{\arraystretch}{1.2} \setlength{\arrayrulewidth}{3\arrayrulewidth} \begin{tabu}{*{3}{|c}|} \taburulecolor{gray!60} \hline \phantom{88} & \phantom{88} & \phantom{88} \tabularnewline \hline \phantom{88} & 5 & 3 \tabularnewline \hline + & 3 & 4 \tabularnewline \tabucline[1.2\arrayrulewidth black]{-} \phantom{88} & 8 & 7 \tabularnewline \hline \end{tabu} }$
} \end{center} \end{minipage}\begin{minipage}{.495\textwidth} \begin{center}
b)~~~~{\huge
${ \renewcommand{\arraystretch}{1.2} \setlength{\arrayrulewidth}{3\arrayrulewidth} \begin{tabu}{*{3}{|c}|} \taburulecolor{gray!60} \hline \phantom{88} & \phantom{88} & \phantom{88} \tabularnewline \hline \phantom{88} & 6 & 3 \tabularnewline \hline + & 3 & 6 \tabularnewline \tabucline[1.2\arrayrulewidth black]{-} \phantom{88} & 9 & 9 \tabularnewline \hline \end{tabu} }$
} \end{center} \end{minipage}
----------------------------------------------------------
Number of pages

Wanda started reading a book at the beginning of page 14. After two hours she finished at the end of page 75. \\ a) How many pages did she read? \\ b) How many pages did she read on averege in one hour?
{\bf Command} \verb|insert| {\bf inserts just after the text of the problem.}

If Wanda started reading at the beginning of page 1 and finished at the end of page 2, how many pages would she read?

Wanda read 62 pages, her average rate was 31 pages per hour.
----------------------------------------------------------
Plums

John had 33 plums. Then he ate one-third of them. How many plums has John now?
~\\ {\bf Add 3cm vertical space...}

How much is 33:3? Answer: 11.

John has 22 plums.
----------------------------------------------------------
Apples

Mark had 40 apples. John took half of Mark's apples and added them to his own stock. Then it turned out that John has 6 times as many apples as Mark. How many apples do John and Mark have together?

How many apples are left in Mark's stock? Answer: 20.

How many apples does John have? Answer: 120.

John and Mark togeher have 140 apples.
----------------------------------------------------------
Pebbles

Daria and Nela collected some pebbles on the beach. If Daria gave Nela  $10$ pebbles, then each girl would have the same number of pebbles. However, if Nela gave Daria  $4$ pebbles, then Daria would have  $5$ times as many pebbles as Nela. How many pebbles did have each of the girls?
~\\ {\bf Change difficulty to change number of points for a problem. Add a grid.}

$D - 10 = N + 10$ and $D + 4 = 5 ( N - 4 )$

Daria had  $31$ pebbles and Nela  $11$ pebbles.
----------------------------------------------------------
~\\ \textbf{insert-before demonstration \\ \emph{Blah, blah, blah...}} \\[-1em]
Sides of rectangles

Calculate the length of: \\ a) a side of the square with area 64 m$^2$. \\b) a side of the rectangle with area 40 m$^2$, and with the second side of length 8~m. \\c) a side of the square with perimeter equal to 20~m. \\ d) a side of the rectangle with perimeter equal to 40~m, and with the second side of length 5~m.

~\\ a) $A = a a = a^2$ \\b)  $A = a b$ \\c)  $L = 4 a$ \\d)  $L = 2( a + b )$

~\\ a) 8 m. \\b) 5 m. \\c) 5 m. \\d) 15 m.
----------------------------------------------------------
Cycling speed

Max went by bike from the starting line and rode at the average speed 4.8 m/s. Ann started from the same line 12 s after Max and she finished the race 24 s before Max. Both, Ann and Max, travelled the same distance. What was the Ann's average speed if the total time of her ride was equal to 576 s?
~\\[5ex] A problem with \verb|-dpc| at the end of its id has control of the maximal number of decimal places (set it in the 4th line in the .gzm file for the whole set)

How much time was Max biking? Answer: 612 s.

What was the length of the route? (Max...) Answer: 2937.6 m.

Ann was cycling with speed 5.1 m/s.
----------------------------------------------------------
Accelerating airplane

An airplane, initially at rest in the airport, started to move along a runway with the constant acceleration equal to $7.8$ m/s$^2$. Calculate the airplane's speed after the time of $6$ s.
~\\ {\bf Problems can be repeated.}

$v = a t$

$46.8$ m/s
----------------------------------------------------------
~\\ \textbf{\emph{Again the same problem.}} \\[-1em]
Accelerating airplane

An airplane, initially at rest in the airport, started to move along a runway with the constant acceleration equal to $4.3$ m/s$^2$. Calculate the airplane's speed after the time of $6$ s.

$v = a t$

$25.8$ m/s
----------------------------------------------------------
~\\ \needspace{3\baselineskip} \textbf{\emph{And again the same problem.}} \\[-1em]
Accelerating airplane

An airplane, initially at rest in the airport, started to move along a runway with the constant acceleration equal to $4.9$ m/s$^2$. Calculate the airplane's speed after the time of $5$ s.

$v = a t$

$24.5$ m/s