Formula for speed

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In order to access this I need to be confident with:

Arithmetic Converting units of time Converting metric units Conversion of units

This topic is relevant for:

GCSE Maths Ratio and Proportion Compound Measures Speed Distance Time

Formula For Speed

Here we will learn about the formula for speed including understanding and using the terms constant speed and average speed. We will also be calculating the average speed of an object given its distance and time. This will extend to using and applying the speed formula and solving problems involving the formula for speed.

There are also worksheets on the formula for speed distance and time based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is the formula for speed?

The formula for speed is given by

Speed $\textbf{=}$ distance $\textbf{÷}$ time

“Speed equals distance divided by time”

You will normally shorten this to the below:

The speed of an object is travelling at is related to the distance it is covering in relation to how long it was travelling for (time).

What is the formula for speed?

What is speed?

Speed is about how fast an object moves. The speed of the moving object is found by calculating the relationship between the distance the object travels and the period of time taken to travel the distance.

Some examples of the units of speed are:

Metres per second $(m/s)$
Miles per hour $(mph)$
$Km$ per hour $(km/h)$
Speed of sound $343$ metres per second
Speed of light $299 \ 792 \ 458$ metres per second

Constant speed is where the speed does not change, e.g. a straight line on a distance-time graph indicates a constant speed.

We can calculate the average speed of an object by dividing the total distance by the total time.

If you also consider the direction of the movement as well at its speed then this is called the object’s velocity.

What is time?

Time can be defined as the ongoing sequence of events taking place.

Some examples of the units of time are:

Seconds $(sec)$
Minutes $(mins)$
Hours $(hrs)$
Days

Note: The $SI$ unit (Standard Unit Measurement) for time is a second.

What is distance?

Distance is the length of space between two points.

Some examples of the units of distance are:

Millimetres $(mm)$
Centimetres $(cm)$
Metres $(m)$
Kilometres $(km)$
Miles

Note: if we only consider how far the object has moved in regards to its starting point this is called displacement.

Rate of change

The speed of an object is the rate of change between the distance covered and the amount of time taken. When working with graphs the rate of change can be found by calculating the gradient of the distance-time graph.

This page focused specifically on speed. If you want to focus on speed, distance, time please follow the link below.

Step-by-step guide: Speed distance time (coming soon)

How to use the formula for speed

In order to use the formula for speed:

Write down which variable you know with their units.
Check the units align, do any need to be converted?
Write down the formula for speed.
Solve to find speed (or distance or time).
Clearly state your answer with the correct units.

Explain how to use the formula for speed

Speed distance time worksheet

Get your free speed distance time worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Speed distance time worksheet

Get your free speed distance time worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on compound measures

Formula for speed is part of our series of lessons to support revision on compound measures. You may find it helpful to start with the main compound measures lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Formula for speed examples

Example 1: calculating speed by substituting values into the speed formula

Question: A car travels at a constant speed. The train travels $100 \ miles$ in $2 \ hours.$

Give your answer in miles per hour $(mph)$

Write down which variable you know with their units.

Speed: unknown

Distance: $100 \ miles$

Time: $2 \ hours$

2Check the units align, do any need to be converted?

Units are correct as the questions’ units are already in miles and hours.

3Write down the formula for speed.

\text{Speed } = \text{ distance } \div \text{ time}

4Solve to find speed (or distance or time).

We are finding the speed.

\begin{aligned} \text{Speed} &= \text{distance}\div \text{time} \\\\ \text{Speed} &= 100\ \text{miles}\div 2\ \text{hours} \\\\ \text{Speed} &= 50\ \text{miles per hour} \ \text{(mph)} \end{aligned}

5Clearly state your answer with the correct units.

The car travels at $50 \ miles \ per \ hour \ (mph)$

Example 2: calculating speed by substituting values into the speed formula

Question: A train travels at a constant speed. The train travels a total distance of $450 \ km$ in a period of time of $4 \ hours.$

Give your answer in kilometre per hour $(km/h)$

Write down which variable you know with their units.

Speed: unknown

Distance: $450 \ km$

Time: $4 \ hours$

Check the units align, do any need to be converted?

Units are correct as the questions’ units are already in kilometres and hours.

Write down the formula for speed.

\text{Speed } = \text{ distance } \div \text{ time}

Solve to find speed (or distance or time).

We are finding the speed.

$\begin{aligned} \text{Speed} &= \text{distance}\div \text{time} \\\\ \text{Speed} &= 450\ \text{km}\div 4\ \text{hours} \\\\ \text{Speed} &= 112.5 km/h \end{aligned}$

Clearly state your answer with the correct units.

The car travels at $112.5 \ km/h$

Example 3: calculating speed by substituting values into the speed formula with unit conversion

Question: A person walks at a constant speed. They travel $600 \ m$ in $0.25 \ hours.$

Give your answer in metres per minute $(m/min)$

Write down which variable you know with their units.

Speed: unknown

Distance: $600 \ m$

Time: $0.25 \ hours$

Check the units align, do any need to be converted?

The answer is asked to be given metres per minute.

The distance is already given in metres so you do not need to convert this unit.

The time is given in hours so you need to convert this to minutes.

$0.25 \ hours \times 60=15 \ minutes$

Speed: unknown

Distance: $600 \ m$

Time: $15 \ minutes$

Write down the formula for speed.

\text{Speed } = \text{ distance } \div \text{ time}

Solve to find speed (or distance or time).

We are finding the speed.

$\begin{aligned} \text{Speed} &= \text{distance}\div \text{time} \\\\ \text{Speed} &= 600\ \text{m}\div 15\ \text{minutes} \\\\ \text{Speed} &= 40 \ m/min \end{aligned}$

Clearly state your answer with the correct units.

The car travels at $40 \ m/min$

Example 4: using speed to find another value

Question: Phil is in a running race. Phil runs at an average speed of $5 \ m/s.$

The race is $21 \ km$ long.

What is the amount of time Phil takes to finish the race?

Give your answer in $hours$ and $minutes.$

Write down which variable you know with their units.

Speed: $5 \ m/s$

Distance: $21 \ km$

Time: unknown

Check the units align, do any need to be converted?

The question used two different units of distance, you need to convert one so you are working with equivalent distances. In this question it is easier to convert $21 \ km$ to $m.$

$21 \ km \times 100=21000 \ m$

Because you now have equivalent units of distances you can calculate Phil’s time before converting to $hours$ and $minutes.$

Write down the formula for speed.

\text{Speed } = \text{ distance } \div \text{ time}

Solve to find speed (or distance or time).

We are finding the time. We need to adapt the speed formula.

\begin{aligned} \text {Time }&=\text { distance } \div \text { speed } \\\\ \text {Time }&=21000 m \div 5 \ m/ s \\\\ \text {Time }&=4200 \text { seconds } \end{aligned}

Clearly state your answer with the correct units.

You have calculated the time to be $4200 \ seconds.$

However the question wants the time in $hours$ and $minutes,$

Remember: $seconds \div 60 = minutes$

$4200 \div 60=70 \ minutes$

Therefore

$70 \ minutes=1 \ hr$ and $10 mins$

Therefore

Phil completes the race in $1 \ hour$ and $10 \ minutes$

Example 5: using speed to find another value

Question: A train travels at $120 \ km/h$ for $3\frac{1}{4} \ hours.$ Calculate the total distance travelled.

Write down which variable you know with their units.

Speed: $120 \ km/h$

Distance: unknown

Time: $3\frac{1}{4} \ hours=3.25 \ hours$

Check the units align, do any need to be converted?

The units align. Sometime people prefer decimals to fractions, so we can use $3\frac{1}{4}$ or $3.25$

Write down the formula for speed.

\text{Speed } = \text{ distance } \div \text{ time}

Solve to find speed (or distance or time).

We are finding the time. We need to adapt the speed formula.

\begin{aligned} \text {Distance }&=\text {speed} \times \text {time} \\\\ \text {Distance }&=120 \ \text{km/h} \times 3.25\ \text{hours} \\\\ \text {Distance }&=390 \text { km } \end{aligned}

Clearly state your answer with the correct units.

You have calculated the time to be $390 \ kilometres.$

Therefore the distance of the journey is $390 \ km.$

Example 6: problem involving speed

Miss Yellow completes a journey in $3$ stages.

In the first stage she travels at $33.75 \ km$ in $45 \ minutes.$

In the second stage she travels $258 \ km$ in $4 \ hours$ and $18 \ minutes.$

The final stage is much shorter and she travels $1200 \ m$ in $90 \ seconds.$

What was her average speed for the whole journey?

Give your answer in $km/min$ to $3$ significant figures.

Write down which variable you know with their units.

You want to know Miss Yellow’s overall average speed so you need to calculate her total distance and total time

Speed: unknown

Distance: $33.75 \ km + 258 \ km + 1200 \ m$

Time: $45 \ minutes + 4 \ hours$ and $18 \ minutes + 90 \ Seconds$

Check the units align, do any need to be converted?

You will notice in the above the units are not the same for distance or speed. You need to convert them all first before proceeding.

Distance: convert all to $km$

$1200 \ m = 1.2 \ km$

Therefore total distance is

$33.75 \ km + 258 \ km + 1.2 \ km = 292.95$

Time: convert all to $minutes$

$4 \ hours$ and $18 \ minutes = 258 \ minutes$

$90 \ seconds = 1.5 \ minutes$

Therefore total time is

$45 \ minutes + 258 \ minutes + 1.5 \ minutes =304.5 \ minutes$

Write down the formula for speed.

\text{Speed } = \text{ distance } \div \text{ time}

Solve to find speed (or distance or time).

\begin{aligned} \text{Speed} &= \text{distance}\div \text{time} \\\\ \text{Speed} &= 292.95 \ \text{km}\div 305.5 \ \text{minutes} \\\\ \text{Speed} &= 0.96206... km/min \end{aligned}

Clearly state your answer with the correct units.

$0.96206... \ km/min$ needs to be rounded to $3$ significant figures

The car travels at $0.962 \ km/min$

Common misconceptions

Incorrect formula for speed

You must remember the speed formula with the correct operations between distance and time.

$\text{Speed } = \text{ distance } \div \text{ time}$

Units

You must remember the relationship between the units is important for the context of the question. If you are given an object’s speed in km per hour and the time as minutes you need to first convert one of the units to be able to give an answer in hours.

E.g. $km/h \div minutes$ does not give you $km$

Check if you answer is ‘sensible’

If you have found the speed of a car is $300 \ mph$ you have most likely made an error as this answer is not ‘sensible’ within the context of the question as it is too high speed for a car. This is a useful (and quick) way of checking your answer.

Practice formula for speed questions

720 \ km/h

80 \ km/h

0.0125 \ km/h

80000 \ m/hour

\begin{aligned} \text{Speed } &= \text{ distance } \div \text{ time} \\\\ \text { Speed }&=240 \mathrm{~km} \div 3 \text { hours } \\\\ \text { Speed }&=80 \mathrm{~km} / \mathrm{h} \end{aligned}

100 \ m/h

2500 \ m/h

0.01 \ m/h

0.1 \ km/h

\begin{aligned} \text{Speed } &= \text{ distance } \div \text{ time} \\\\ \text { Speed }&=500 \ \mathrm{m} \div 5 \text { hours } \\\\ \text { Speed }&=100 \ \mathrm{m} / \mathrm{h} \end{aligned}

400 \ m/h

2500 \ m/h

0.4 \ km/h

2.5 \ km/h

1200 \ m=1.2 \ km

\text{Speed } = \text{ distance } \div \text{ time}

\begin{aligned} \text { Speed }&=1.2 \ \mathrm{km} \div 3 \text { hours } \\\\ \text { Speed }&=0.4 \ \mathrm{km} / \mathrm{h} \end{aligned}

30 \ m/h

1.8 \ m/min

1800 \ m/min

30 \ m/min

\begin{aligned} 0.5 \text { hours }&=30 \text { minutes } \\\\ \text { Speed }&=\text { distance } \div \text { time } \\\\ \text { Speed }&=900 \ m \div 30 \text { minutes } \\\\ \text { Speed }&=30 \ \mathrm{m} / \mathrm{min} \end{aligned}

270 \ miles

4.5 \ miles

9 \ miles

45 \ miles

90 \ minutes = 1.5 \ hours

\begin{aligned} \text {Distance }&=\text {speed} \times \text {time} \\\\ \text {Distance }&=3 \times 1.5 \\\\ \text {Distance }&=4.5 \ \text{miles} \end{aligned}

300 \ minutes

50 \ minutes

3 \ minutes

5 \ minutes

\begin{aligned} \text {Time}&=\text {distance} \div \text {speed} \\\\ \text {Time}&=1800 \ \mathrm{m} \div 6 \text { m/s } \\\\ \text {Time}&=300 \ \mathrm{sec} \end{aligned}

$300 \ seconds$ is $5 \ minutes$

Formula for speed GCSE questions

1. Emily drives her car $186 \ kilometres$ in $3 \ hours.$ What is her average speed?

(2 marks)

Show answer

186 \div 3

(1)

62

(1)

2. Jenny left her home at $9am$ and walked to the library. She arrived at $10:30am.$ The library is $3 \ miles$ from her house.

(a) What was Jenny’s average speed?

(b) On the return journey she takes a longer route home which is $2 \ miles$ longer than before. She takes $2 \ hours$ to walk home.

On which journey was Jenny walking faster?

You must show your workings.

(5 marks)

Show answer

(a)

1.5

(1)

3 \div 1.5

(1)

2

(1)

(b)

2.5 \ mph

(1)

Faster walking to the library

(1)

3. Seobin was driving to a hotel.

He looked at his Sat Nav at $12:30,$ it said he had $66 \ km$ left for his journey.

Seobin arrived at the hotel at $15:48$

Work out his average speed between $12:30$ and $15:48$

(4 marks)

Show answer

Attempt to find the time taken for the journey

(1)

$3 \ hours \ 18 \ minutes$ or $3.3 \ hours$

(1)

66 \div “3.3”

(1)

20

(1)

Learning checklist

You have now learned how to:

Use compound units such as speed

Solve simple kinematic problem involving distance and speed

Change freely between related standard units (eg time, length) and compound units (e.g. speed) in numerical contexts

Work with compound units in a numerical context

The next lessons are

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