Using compound units - speed - Numbas at mathcentre.ac.uk

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Christian Lawson-Perfect

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Christian Lawson-Perfect

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7 years, 8 months ago

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Split off from a larger question.

Heavily edited the advice to make sure no weird rounding errors happen, and fixed a fair bit of grammar.

The question now picks a physically reasonable speed and generates a time based on that.

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Christian Lawson-Perfect 7 years, 8 months ago

Created this as a copy of Using compound units: price/weight of sweets.

Name	Status	Author	Last Modified
Using compound units: price/weight of sweets	Ready to use	Elliott Fletcher	19/12/2022 12:21
Using compound units - speed	Ready to use	Christian Lawson-Perfect	20/11/2019 14:44
Using compound units - room hire price per hour and per minute	Ready to use	Christian Lawson-Perfect	20/12/2022 12:55
David's copy of Using compound units - room hire price per hour and per minute	draft	David Rickard	07/11/2018 21:05
David's copy of Using compound units: price/weight of sweets	draft	David Rickard	07/11/2018 21:05
David's copy of Using compound units - speed	draft	David Rickard	07/11/2018 21:05
David's copy of Using compound units - speed	draft	David Rickard	07/11/2018 21:06

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Question statement

An athlete runs $\var{distance}$ m in $\var{seconds}$ seconds.

Round each of your answers to two decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

distance	integer	80
seconds	integer	15
speed	number	5.1388695459

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(80,100,150,200)

JME function reference

Description

Distance that the runner ran.

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`

→ Used by:

seconds

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
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Part b) Gap-fill
1. Gap Number entry
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Gap-fill

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

What was the runner's average speed, in metres per second?

Unnamed gap m/s

Advice

a)

To find the average speed of the runner in meters per second (m/s), we divide the distance covered by the runner (in metres) by the time taken for the runner to run this distance (in seconds).

$\begin{align} \text{Average speed} &= \displaystyle\frac{\var{distance}}{\var{seconds}}\\ &= \var{distance/seconds}\\ &= \var{dpformat(distance/seconds,2)}\; \text{m/s} \; (\text{rounded to $2$ decimal places}). \end{align}$

b)

We can convert the average speed of the runner that we calculated in a) in metres per second to kilometres per hour using the following two equivalences:

$1\text{m} = \displaystyle\frac{1}{1000}\text{km},$

$1 \; \text{second} = \displaystyle\frac{1}{60} \; \text{minutes} = \displaystyle\frac{1}{3600} \; \text{hours}.$

We know from a) that the average speed of the runner in m/s was $\var{dpformat(distance/seconds,5)}$ m/s ( $5$ d.p), so to convert this speed to km/h we first need to convert metres to kilometres,

$\var{dpformat(distance/seconds,5)} \; \text{m/s} = \var{dpformat(distance/seconds/1000,5)} \text{km/s} \; (5 \; \text{d.p})$

Then we convert seconds to hours,

$1 \; \text{second} = \displaystyle\frac{1}{3600} \; \text{hours}.$

Now we have

$\var{dpformat(distance/seconds,5)} \; \text{m/s} = \var{sigformat(distance/seconds/1000,5)} \; \text{kilometres per $\displaystyle\frac{1}{3600}$ hours}.$

We want a rate per one hour, so we multiply by $3600$ to obtain a measurement in km/h:

$\begin{align}\var{sigformat(distance/seconds/1000,5)} \; \text{kilometres per $\displaystyle\frac{1}{3600}$ hours} &= \var{siground(distance/seconds/1000,5)*3600} \; \text{km}/\text{h}\\&=\var{dpformat(distance/seconds*3.6, 2)} \; \text{km}/\text{h} \; (\text{rounded to $2$ decimal places}).\end{align}$

$\var{sigformat(distance/seconds/1000,5)} \; \text{kilometres per $\displaystyle\frac{1}{3600}$ hours} = \var{distance/seconds*3.6} \; \text{km}/\text{h}.$

Note that throughout this calculation we have rounded all figures to $5$ decimal places for convenience; when doing calculations which involve long decimals, you should always input the full figure into your calculator to avoid getting an incorrect answer due to rounding.

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Using compound units - speed

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Checkpoint description

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Using compound units - speed

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`