Speed, distance, time; rounding and significant figures

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David Rickard 6 years, 5 months ago

Created this as a copy of Converting units of length (km/m/miles).

Name	Status	Author	Last Modified
Converting units of length (km/m/miles)	Ready to use	Chris Graham	20/11/2019 14:36
Speed, distance, time; rounding and significant figures	draft	David Rickard	16/10/2022 20:22

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Question statement

{person['name']} is training for the {location} Marathon.

Give any introductory information the student needs.

			Name	Type	Generated Value

km	integer	28
person	dict	Dictionary with 3 entries
location	string	London
mins	integer	2
maxspeed	rational	28499/7290
bestseconds	decimal	dec("10792")
bestmins	decimal	dec("60")
besthours	decimal	dec("3")
bestpace	decimal	dec("3.91")
worstspeed	rational	27500/7349
worstpace	decimal	dec("3.74")
dechours	decimal	dec("2.998")
decmins	decimal	dec("59.88")
recordmins	integer	6
recordpace	decimal	dec("5.58")
headstart	number	12.6

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(24..28#2)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

The week before the event, {person['name']} goes on a final training run. An app on {person['pronouns']['their']} phone tells {person['pronouns']['them']} that {person['pronouns']['they']} ran $\var{km}$ km, a distance that is accurate to the nearest whole kilometer.

What was the minimum length, in metres, of {person['pronouns']['their']} training run?

Gap 0. metres.

What was the maximum length, in metres, of {person['pronouns']['their']} training run?

Gap 1. metres.

Give your answers correct to the nearest whole number.

Advice

a)

{person['name']}'s training run is $\var{km}$ km long.

To convert $\var{km}$ km into metres, we multiply $\var{km}$ by $1000$.

\[\var{km}\times1000= \var{km*1000}\text{ metres.}\]

Rounding to the nearest whole kilometer means the app would round anything $\var{km*1000-500}\,$m or higher up to $\var{km}\,$km, and anything up to $\var{km*1000+499}\,$m would be rounded down to ${\var{km}\,$km.

b)

{person['name']}'s training run lasted $2\,$hours and $\var{mins}\,$minutes.

To convert $2\,$hours to minutes, we multiply by $60$. To convert these minutes to seconds, we multiply by $60$ again:

\begin{align}
2\,\text{hours}\times60&=120\,\text{minutes}\\
120\,\text{minutes}\times60&=7200\,\text{seconds}
\end{align}

and to convert $\var{mins}\,$minutes to seconds, we multiply by $60$:

\[\var{mins}\,\text{minutes}\times60=\var{mins*60}\,\text{seconds}\]

Giving us a total of $7200+\var{mins*60}=\var{7200+mins*60}\,$seconds.

Since $\var{mins}\,$minutes was given as being correct to the nearest minute, we know that it in fact represents possible times from $\var{mins-1}\,$minutes and $30$ seconds to $\var{mins}\,$minutes and $29\,$seconds, so in fact our total should be between $\var{(120+{mins})*60-30}$ and $\var{(120+{mins})*60+29}\,$seconds.

c)

To calculate a running pace in metres per second, we simply use:

\[\text{Speed}=\frac{\text{Distance}}{\text{Time}}\]

Our greatest value for speed will involve the longest distance in the shortest time; and our lowest value for speed will involve the shortest distance in the longest time.

Highest pace:

\[\frac{\var{({km}*1000+499)}\,\text{metres}}{\var{((120+{mins})*60-30)}\,\text{seconds}}=\var{bestpace}\,\text{m/s}\]

Lowest pace:

\[\frac{\var{({km}*1000-500)}\,\text{metres}}{\var{((120+{mins})*60+29)}\,\text{seconds}}=\var{worstpace}\,\text{m/s}\]

d)

If they can maintain a pace of $\var{bestpace}\,$m/s, then their race time will be:

\[\text{Time}=\frac{\text{Distance}}{\text{Speed}}=\frac{42195\,\text{metres}}{\var{bestpace}\,\text{m/s}}=\var{bestseconds}\,\text{seconds}\]

If we divide by $60$, we will get the number of minutes; dividing by $60$ again gets us the number of hours:

\[\frac{\var{bestseconds}\,\text{seconds}}{60\times60}=\var{dechours}\,\text{hours}=\var{besthours}\,\text{hours and }\var{decmins}\,\text{mins}\]

(Don't forget that $\var{dechours-besthours}$ hours means $\var{dechours-besthours}\times60\,$minutes, not $\var{(dechours-besthours)*100}\,$minutes.)

e)

First convert to minutes and seconds by multiplying by $60$:

\[2\,\text{hours and }\var{recordmins}\,\text{minutes}=\var{120+recordmins}\,\text{minutes}\times60=\var{(120+recordmins)*60}\,\text{seconds}\]

So the impressive runner will cover the whole course in this length of time. Meanwhile, {person['name']}'s best pace is $\var{bestpace}\,$m/s. So during this time they could cover a distance of $\var{(120+recordmins)*60}\times\var{bestpace}=\var{(120+recordmins)*60*bestpace}\,$metres.

This means that {person['name']} needs a head start of $42195-\var{(120+recordmins)*60*bestpace}=\var{42195-(120+recordmins)*60*bestpace}\,$metres or $\var{headstart}\,$km.

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

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This question is used in the following exams:

Week 3 Assessment by David Rickard in PHYS1010.
Linear and Projectile Motion by David Rickard in PHYS1010.
One Dimensional Motion by David Rickard in PHYS1010.

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Speed, distance, time; rounding and significant figures

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

David Rickard 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

e)

Loading...

Error

Speed, distance, time; rounding and significant figures

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

David Rickard 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

e)

Generated value: `integer`