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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.
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).
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:
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.
Time can be defined as the ongoing sequence of events taking place.
Some examples of the units of time are:
Note: The SI unit (Standard Unit Measurement) for time is a second.
Distance is the length of space between two points.
Some examples of the units of distance are:
Note: if we only consider how far the object has moved in regards to its starting point this is called displacement.
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)
In order to use the formula for speed:
Get your free speed distance time worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free speed distance time worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEFormula 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:
Question: A car travels at a constant speed. The train travels 100 \ miles in 2 \ hours.
Give your answer in miles per hour (mph)
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)
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.
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
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.
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
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.
Solve to find speed (or distance or time).
We are finding the time. We need to adapt the speed formula.
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
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.
Solve to find speed (or distance or time).
We are finding the time. We need to adapt the speed formula.
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.
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.
Solve to find speed (or distance or time).
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
You must remember the speed formula with the correct operations between distance and time.
\text{Speed } = \text{ distance } \div \text{ time}
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
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.
1. Find the speed of an object which travelled 240 \ km in 3 \ hours. Give your answer in km/h
2. Find the speed of an object which travelled 500 \ m in 5 \ hours. Give your answer in m/h
3. Find the speed of an object which travelled 1200 \ m in 3 \ hours. Give your answer in km/h
\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}
4. A person walks at a constant speed. They travel 900 \ m in 0.5 \ hours. Calculate the speed. Give your answer in metres per minute (m/min)
5. A person walks at a constant speed of 3 miles per hour. They walk for 90 \ minutes. Calculate how far they walk.
\begin{aligned} \text {Distance }&=\text {speed} \times \text {time} \\\\ \text {Distance }&=3 \times 1.5 \\\\ \text {Distance }&=4.5 \ \text{miles} \end{aligned}
6. An object travels 1800 \ m at a speed of 6m/s. Calculate the time taken. Give you anwer in minutes.
300 \ seconds is 5 \ minutes
1. Emily drives her car 186 \ kilometres in 3 \ hours. What is her average speed?
(2 marks)
(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)
(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)
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)
You have now learned how to:
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