Compound measures combine two different units to describe how one quantity changes in relation to another. Common compound measures include speed and fuel consumption, which are widely used in real life contexts.

 

 

Speed

Speed measures how far something travels in a given time.

 

Speed is calculated using the formula:
$$
speed = \frac{distance}{time}
$$

 

Because it compares distance with time, speed is a compound measure.

 

Common units of speed include:
• \( m/s \) metres per second
• \( km/h \) kilometres per hour
• \( mph \) miles per hour

 

 

Interpreting Speed

A speed of \( 10\ m/s \) means an object travels 10 metres every second.

 

A speed of \( 60\ km/h \) means an object travels 60 kilometres in one hour.

 

A speed of \( 30\ mph \) means an object travels 30 miles in one hour.

 

Larger numerical values do not always mean greater speed unless the units are the same.

 

 

Converting Between Speed Units

Speeds may need to be converted between different units.

 

For example:
• converting \( km/h \) to \( m/s \)
• converting \( mph \) to \( km/h \)

 

The appropriate conversion values will be given in questions.

 

Always:
• convert distance units
• convert time units
• then calculate the speed

 

 

Fuel Consumption

Fuel consumption measures how efficiently fuel is used.

 

A common unit of fuel consumption is:
• \( mpg \) miles per gallon

 

Fuel consumption is calculated using:
$$
fuel\ consumption = \frac{distance}{fuel\ used}
$$

 

 

Interpreting Fuel Consumption

A fuel consumption of \( 40\ mpg \) means a vehicle travels 40 miles using one gallon of fuel.

 

A higher mpg value means better fuel efficiency, because more distance is travelled per unit of fuel.

 

A lower mpg value means poorer fuel efficiency.

 

Fuel consumption problems often involve:
• distance travelled
• fuel used
• comparing efficiency between vehicles

 

 

Using Compound Measures in Problems

When solving problems involving speed or fuel consumption:

• identify the quantities given
• check that units are consistent
• substitute values into the correct formula
• include the correct compound unit in the answer

 

Always write units clearly with your final answer

 

 

Key Points to Remember

Compound measures combine two different units.
Speed is calculated using distance divided by time.
Common speed units include \( m/s \), \( km/h \) and \( mph \).
Fuel consumption is often measured in \( mpg \).
Higher mpg values indicate greater fuel efficiency.

 

Being confident with compound measures allows real life situations involving movement and efficiency to be interpreted and calculated accurately.