MATHEMATICSCompound Units - Speed

Lesson Objectives

•The aim of this powerpoint is to help you…

• Use the link between speed, distance and time to solve problems

Compound Measures• Compound measures are measurements involving more

than one type of unit

• Speed is an example of a compound measure. • It could be measured in miles per hour. • It is therefore a mix (or compound) of distance (or length)

(e.g. miles) and time (e.g. hours)

• The ‘per’ in-between the miles and the hour shows you divided a distance by a time to get a speed.

Formula Triangles

• To help re-arrange formulas involving exactly three variables and only division or multiplication, we can use a formula triangle

• To use them, cover the variable you want to find with your thumb and work out the formula as follows:

• The top value is divided by either of the bottom values or the bottom values are multiplied together.

• In this triangle…• cover x to find it equals yz

(on the bottom), ie x = yz• cover y to find it equals x on

the top divided by z on the bottom, ie y=x/z and so on…

x

y z

Speed, Distance and Time• To find the formula triangle for speed, distance and time,

look for the units of the compound measure

• Speed can be measured in metres per second

Thus: Speed = distance ÷ time

Divide TOP by BOTTOM

SDT Formula Triangle

Formulae:

S = D ÷ T

D = ST (ie. S × T)

T = D ÷ S

D

S T

Don’t forget to cover theletter of the variable youare trying to find!

Units• When answering questions please be careful about the

units you use they must be compatible!

• If your distance is metres and time is seconds then the speed units are metres per second

• If your speed is in km per hour and distance is in km, then time is in hours

• If time is in hours and speed is in metres per minute, then a conversion is needed before calculating distance and its units!

SDT Problems – Quick Practice• What speed am I travelling at if I travel 90 miles in 3

hours?

• How long does it take to travel 140 miles at an average speed of 40mph?

• How far can you travel in 3 hours at an average speed of 56 miles per hour?

• Work out your answers before clicking on to the next slide

SDT Problems - Answers• What speed am I travelling at if I travel 90 miles in 3

hours?S = D ÷ T 90 miles ÷ 3 hours = 30 mph

• How long does it take to travel 140 miles at an average speed of 40mph?T = D ÷ S 140 miles ÷ 40mph = 3½ hrs

• How far can you travel in 3 hours at an average speed of 56 miles per hour?

• D = S × T 56mph × 3h = 168 miles

Compound Measure Conversions

Step-by-Step guide to converting:

(1) (Use the formula triangle to) write out the formula including units

(2) Convert each unit as required

(3) Carry out the calculation

Conversions – Example 1

Change 36km per hour to metres per second

(1) Speed = distance ÷ time

Speed = 36km ÷ 1 hour

(2) (36 km 36 000m) (1 h 60 m 3600s)

(3) Speed = 36 000m ÷ 3600 s = 10m/s

What next?• Print out the notes called Speed. Read through them and

make sure you answer any questions.

• Work through the MyMaths lesson and its online homework called Speed found at:

• http://app.mymaths.co.uk/296-resource/speed• http://app.mymaths.co.uk/296-homework/speed

• Save and complete the worksheet: SDT-S1.xlsx

• Now move on to the PAV1 powerpoint