Question

1. explain what a derived unit is. give two examples other than km/h. 2 marks

1. convert 108 km/h to m/s. show your working. 2 marks

Explanation:

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<reasoning>

Convert the time values

Using the Metric Conversion and Unit Conversion Rates knowledge points:

• For part (a):

Convert \(2.75\text{ hours}\) to hours and minutes.
The whole number of hours is \(2\text{ h}\).
Convert the remaining \(0.75\text{ hours}\) to minutes:
\[0.75 \times 60\text{ min/h} = 45\text{ min}\]
So, \(2.75\text{ hours} = 2\text{ h } 45\text{ min}\).

• For part (b):

Convert \(4500\text{ milliseconds}\) to seconds.
Since \(1\text{ second} = 1000\text{ milliseconds}\):
\[\frac{4500}{1000} = 4.5\text{ s}\]

• For part (c):

Convert \(3\text{ days } 4\text{ hours}\) to hours.
Since \(1\text{ day} = 24\text{ hours}\):
\[3 \times 24\text{ hours} + 4\text{ hours} = 72 + 4 = 76\text{ hours}\]

Define derived units and provide examples

Using the Derived Units knowledge point:

• Definition:

A derived unit is a unit of measurement obtained by combining one or more base units through multiplication or division.

• Examples:

Two common examples other than \(\text{km/h}\) are:

1. Meters per second (\(\text{m/s}\)) for speed.
2. Grams per cubic centimeter (\(\text{g/cm}^3\)) or kilograms per cubic meter (\(\text{kg/m}^3\)) for density.

Convert speed units

Using the Unit Conversion Rates knowledge point:

• Convert \(108\text{ km/h}\) to \(\text{m/s}\).

Convert kilometers to meters:
\[108\text{ km} = 108 \times 1000\text{ m} = 108,000\text{ m}\]
Convert hours to seconds:
\[1\text{ h} = 3600\text{ s}\]
Calculate the speed in \(\text{m/s}\):
\[\frac{108,000\text{ m}}{3600\text{ s}} = 30\text{ m/s}\]
</reasoning>

<answer>

Question 5

(a) \(2.75\text{ hours} = 2\text{ h } 45\text{ min}\)
(b) \(4500\text{ milliseconds} = 4.5\text{ s}\)
(c) \(3\text{ days } 4\text{ hours} = 76\text{ hours}\)

Question 6

• Definition: A derived unit is a unit of measurement formed by combining base units (such as meters, kilograms, or seconds) using multiplication or division.
• Examples:

1. Meters per second (\(\text{m/s}\))
2. Kilograms per cubic meter (\(\text{kg/m}^3\))

Question 7

\[108\text{ km/h} = \frac{108 \times 1000\text{ m}}{3600\text{ s}} = 30\text{ m/s}\]
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Answer:

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<reasoning>

Convert the time values

Using the Metric Conversion and Unit Conversion Rates knowledge points:

• For part (a):

Convert \(2.75\text{ hours}\) to hours and minutes.
The whole number of hours is \(2\text{ h}\).
Convert the remaining \(0.75\text{ hours}\) to minutes:
\[0.75 \times 60\text{ min/h} = 45\text{ min}\]
So, \(2.75\text{ hours} = 2\text{ h } 45\text{ min}\).

• For part (b):

Convert \(4500\text{ milliseconds}\) to seconds.
Since \(1\text{ second} = 1000\text{ milliseconds}\):
\[\frac{4500}{1000} = 4.5\text{ s}\]

• For part (c):

Convert \(3\text{ days } 4\text{ hours}\) to hours.
Since \(1\text{ day} = 24\text{ hours}\):
\[3 \times 24\text{ hours} + 4\text{ hours} = 72 + 4 = 76\text{ hours}\]

Define derived units and provide examples

Using the Derived Units knowledge point:

• Definition:

A derived unit is a unit of measurement obtained by combining one or more base units through multiplication or division.

• Examples:

Two common examples other than \(\text{km/h}\) are:

1. Meters per second (\(\text{m/s}\)) for speed.
2. Grams per cubic centimeter (\(\text{g/cm}^3\)) or kilograms per cubic meter (\(\text{kg/m}^3\)) for density.

Convert speed units

Using the Unit Conversion Rates knowledge point:

• Convert \(108\text{ km/h}\) to \(\text{m/s}\).

Convert kilometers to meters:
\[108\text{ km} = 108 \times 1000\text{ m} = 108,000\text{ m}\]
Convert hours to seconds:
\[1\text{ h} = 3600\text{ s}\]
Calculate the speed in \(\text{m/s}\):
\[\frac{108,000\text{ m}}{3600\text{ s}} = 30\text{ m/s}\]
</reasoning>

<answer>

Question 5

(a) \(2.75\text{ hours} = 2\text{ h } 45\text{ min}\)
(b) \(4500\text{ milliseconds} = 4.5\text{ s}\)
(c) \(3\text{ days } 4\text{ hours} = 76\text{ hours}\)

Question 6

• Definition: A derived unit is a unit of measurement formed by combining base units (such as meters, kilograms, or seconds) using multiplication or division.
• Examples:

1. Meters per second (\(\text{m/s}\))
2. Kilograms per cubic meter (\(\text{kg/m}^3\))

Question 7

\[108\text{ km/h} = \frac{108 \times 1000\text{ m}}{3600\text{ s}} = 30\text{ m/s}\]
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