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KS3 Science · Year 7Chapter 11 · Speed, distance-time and weight
Year 7 · Chapter 11

Speed, distance-time and weight

By the end of this chapter you will be able to

  • Calculate speed from distance and time, with the unit m/s
  • Read a distance-time graph: a flat line is stopped, a steeper line is faster
  • Find the speed from the gradient of a straight section of a distance-time graph
  • Explain the difference between mass and weight, and their units
  • Calculate weight from mass, using weight = mass x gravitational field strength (10 N/kg on Earth)

You should already know

  • Measuring time with a stopwatch, and distance with a ruler or metre stick (Chapter 1 of this book)
  • Forces push and pull, from primary school science

Where this leads

  • Forces, moments and pressure, which build on weight and forces (Chapter 12)

National Curriculum for England, Key Stage 3 science, Year 7. Content: P1 speed = distance / time; distance-time graphs, and the gradient of a distance-time graph as the speed, P2 weight and mass: weight = mass x gravitational field strength, measured in newtons; the difference between mass and weight.

Exercise P  Do you remember?

1
FWhat is 60 divided by 3? Write the number.
2
FHow many grams are in 1 kilogram? Write the number.
3
FWhat is the unit of time that we use in science experiments most often? Write the word.
4
FWhat is 12 divided by 4? Write the number.
5
FWhat is 4 times 25? Write the number.
11.1

Speed = distance divided by time

Year 7
P1: speed = distance / time, with the units m/s (metres per second) for speed
Video lesson: Speed = distance divided by timeComing soon
Story. Omar times a runner on the school field. The runner covers 100 metres in 20 seconds. “How fast was the runner going?” asks Omar. His teacher says, “Work out how far was covered each second. That is the speed.”

Speed tells us how far an object moves in each second. It is found using:

speed = distance / time

Distance is measured in metres (m) and time in seconds (s), so speed is in metres per second (m/s). A speed of 5 m/s means the object moves 5 metres in each second, on average.

The table gives three moving things, with the distance and time for each.

Moving thingDistance (m)Time (s)Speed (m/s)
a runner100205
a cyclist3003010
a toy car1243

Key ideas

  • speed = distance / time
  • Distance in metres (m) and time in seconds (s) give speed in m/s.
  • The speed found is an average speed for the whole journey.
  • Rearrange: distance = speed x time, and time = distance / speed.
Worked example 11.1.1
A runner covers 100 m in 20 s. What is the speed? Write the number of m/s.

Method. Use speed = distance / time.

  1. Write the values. The distance is 100 m and the time is 20 s.
    100 and 20
  2. Divide. Speed = 100 / 20.
    100 / 20 = 5
  3. Write the answer.
    5 m/s

Check. 5 x 20 = 100. ✓

Worked example 11.1.2
A cyclist travels 300 m in 30 s. What is the speed? Write the number of m/s.

Method. Use speed = distance / time.

  1. Write the values. The distance is 300 m and the time is 30 s.
    300 and 30
  2. Divide. Speed = 300 / 30.
    300 / 30 = 10
  3. Write the answer.
    10 m/s

Check. 10 x 30 = 300. ✓

Worked example 11.1.3
A toy car moves 12 m in 4 s. How far does it go in 1 second, on average? Write the number of metres.

Method. The speed is the distance per second.

  1. Use the formula. Speed = 12 / 4.
    12 / 4 = 3
  2. Read the answer. So the car moves 3 m in each second, on average.
    3 m/s
  3. Write the answer.
    3 m/s

Check. 3 x 4 = 12. ✓

Watch out

Watch out: divide distance by time, not time by distance. Always check the units: metres and seconds give m/s.

Exam tip

Exam tip. Write the formula, put in the numbers with their units, then divide. Give the unit m/s.

Try it (with your teacher, or a grown-up at home). With a grown-up, measure 10 metres along a corridor or a path with a tape measure. Walk it, timing yourself with a stopwatch. Work out your average speed in m/s, using speed = distance / time.

Exercise 11A  Speed = distance divided by time

1
FWhat is the formula for speed? Write the words.
2
FWhat is the unit of speed when distance is in metres and time is in seconds? Write the unit.
3
FA runner covers 100 m in 20 s. What is the speed? Write the number of m/s.
4
FA cyclist covers 300 m in 30 s. What is the speed? Write the number of m/s.
5
FA toy car travels 12 m in 4 s. What is its speed? Write the number of m/s.
6
FA snail moves 2 m in 4 s. What is its speed? Write the number of m/s.
7
PSA child walks 40 m in 80 s. What is the speed? Write the number of m/s.
8
PSA runner covers 50 m in 10 s. How many metres does the runner cover in 1 second, on average? Write the number of metres.
9
PSA car travels 240 m in 20 s. What is its speed? Write the number of m/s.
10
PSRuby runs at 6 m/s for 10 s. How far does she run? Write the number of metres.
11
PSAli says a runner going 100 m in 20 s is faster than a cyclist going 300 m in 30 s. Is Ali right? Write yes or no.
12
PSWorking scientifically: a pupil says the speed of a runner is 20 m/s because the time was 20 s. Explain the mistake. Write one sentence.
13
RChallenge: a car travels at 15 m/s for 8 s. Explain how you would find the distance, and give the number of metres. Write the number of metres.
11.2

Distance-time graphs

Year 7
P1: draw and read distance-time graphs; a flat line means stopped, and a steeper line means faster
Video lesson: Distance-time graphsComing soon
Story. Ali walks along a corridor, stops to talk to a friend, then walks on. His teacher plots his distance from the start against time. “What does the graph tell us?” she asks. “Where he stops, and how fast he goes,” says Ali.

A distance-time graph shows how far an object is from its starting point at each time. Time goes along the horizontal axis, and distance goes up the vertical axis.

A straight line that slopes up means the object is moving at a steady speed. A flat line means the object is stopped. A steeper line means the object is moving faster.

024681001020304050distance from start (m)time (s)stopped
A distance-time graph of a walk: 20 m in 4 s, stopped from 4 to 6 s, then 50 m at 10 s.

The table gives the distance from the start at each time.

Time (s)Distance from start (m)
00
420
620
1050

Key ideas

  • A distance-time graph has time on the horizontal axis and distance on the vertical axis.
  • A flat (horizontal) line means the object is stopped.
  • A straight sloping line means a steady speed.
  • A steeper line means a higher speed.
Worked example 11.2.1
On the graph, how far is Ali from the start at 5 seconds? Write the number of metres.

Method. Read the graph at 5 seconds.

  1. Read the time. At 5 seconds, the line is flat, between 4 and 6 seconds.
    flat
  2. Read the distance. The distance is 20 m, the same as at 4 seconds.
    20
  3. Write the answer.
    20 m

Check. Ali is stopped at this time. ✓

Worked example 11.2.2
Between which two times was Ali stopped? Write the two times.

Method. Find the flat part of the line.

  1. Look for flat. The graph is flat between 4 s and 6 s.
    4 s and 6 s
  2. Write the times. So Ali was stopped from 4 s to 6 s.
    4 s and 6 s
  3. Write the answer.
    4 s and 6 s

Check. The distance does not change while he is stopped. ✓

Worked example 11.2.3
Which part of the graph is steeper: from 0 to 4 s, or from 6 to 10 s? Write the times.

Method. Compare the slopes.

  1. Compare. From 0 to 4 s, Ali covers 20 m. From 6 to 10 s, he covers 30 m.
    20 m and 30 m
  2. Decide. The second part covers more distance in its time, so it is steeper.
    6 s to 10 s
  3. Write the answer.
    6 s to 10 s

Check. A steeper line means a higher speed. ✓

Watch out

Watch out: a flat line does not mean the object has gone back. It means the distance stays the same, so the object is stopped.

Exam tip

Exam tip. When you read a distance-time graph, first look for flat parts (stopped) and then for slopes (moving).

Try it (with your teacher, or a grown-up at home). With a grown-up, walk along a corridor at a steady speed, then stop for a few seconds, then walk on. Ask a helper to mark your distance every 2 seconds on a long strip of paper. Draw the graph and say which part is flat, and which part is steeper.

Exercise 11B  Distance-time graphs

1
FIn a distance-time graph, which quantity goes on the horizontal axis? Write the word: time or distance.
2
FIn a distance-time graph, which quantity goes on the vertical axis? Write the word: time or distance.
3
FWhat does a flat line on a distance-time graph mean? Write the word: moving or stopped.
4
FIs a steeper sloping line a faster or a slower speed? Write the word: faster or slower.
5
FFrom the graph, what is the distance at 10 seconds? Write the number of metres.
6
FFrom the graph, what is the distance at 2 seconds? Write the number of metres.
7
FDoes the distance change between 4 s and 6 s? Write yes or no.
8
PSBetween which two times did Ali walk the furthest, from 0 to 4 s or from 6 to 10 s? Write the times.
9
PSHow far did Ali walk altogether, from 0 s to 10 s? Write the number of metres.
10
PSBen says the graph shows Ali walking backwards at some point. Is Ben right? Write yes or no.
11
PSWorking scientifically: a pupil predicts a steeper line means a faster walk. Describe a test to check this, using a stopwatch. Accept any test that times two walks over the same distance.
12
RChallenge: explain why the line on a distance-time graph becomes flat when an object stops, but does not go back down. Write one sentence.
11.3

Speed from the gradient of a graph

Year 7
P1: the gradient of a distance-time graph gives the speed; find the speed of a straight section by change in distance / change in time
Video lesson: Speed from the gradient of a graphComing soon
Story. Priya wants to know Ali's speed on the walk. “I can read the distance at two times, and divide,” she says. Her teacher says, “You have just found the gradient. For a straight section of the line, the gradient is the speed.”

The gradient of a straight section of a distance-time graph is the speed. It is found using:

gradient = change in distance / change in time

Choose two points on the straight section, read the distances and times, subtract to find the changes, then divide.

The table gives the speed for each part of Ali's walk, from the graph in section 11.2.

From (s)To (s)Change in distance (m)Change in time (s)Speed (m/s)
042045
46020
6103047.5

Key ideas

  • gradient = change in distance / change in time
  • For a straight section, the gradient gives the speed.
  • A flat section has gradient 0, so the speed is 0 m/s.
  • Use two points that are easy to read.
Worked example 11.3.1
From 0 s to 4 s, Ali walks from 0 m to 20 m. What is his speed? Write the number of m/s.

Method. Use gradient = change in distance / change in time.

  1. Find the change in distance. The change in distance is 20 - 0 = 20 m.
    20
  2. Find the change in time. The change in time is 4 - 0 = 4 s.
    4
  3. Divide. Gradient = 20 / 4 = 5, so the speed is 5 m/s.
    20 / 4 = 5
  4. Write the answer.
    5 m/s

Check. 5 x 4 = 20. ✓

Worked example 11.3.2
From 6 s to 10 s, Ali walks from 20 m to 50 m. What is his speed? Write the number of m/s.

Method. Use gradient = change in distance / change in time.

  1. Find the change in distance. The change in distance is 50 - 20 = 30 m.
    30
  2. Find the change in time. The change in time is 10 - 6 = 4 s.
    4
  3. Divide. Gradient = 30 / 4 = 7.5, so the speed is 7.5 m/s.
    30 / 4 = 7.5
  4. Write the answer.
    7.5 m/s

Check. 7.5 x 4 = 30. ✓

Worked example 11.3.3
From 4 s to 6 s, what is Ali's speed? Write the number of m/s.

Method. The line is flat, so the change in distance is zero.

  1. Find the change in distance. The distance is 20 m at both times, so the change is 0.
    0
  2. Divide. Gradient = 0 / 2 = 0, so the speed is 0 m/s.
    0 / 2 = 0
  3. Write the answer.
    0 m/s

Check. A flat line means no movement. ✓

Watch out

Watch out: the gradient uses the change in distance divided by the change in time, not the distances themselves. Subtract the start values first.

Exam tip

Exam tip. Write the two changes first, then divide. Include the unit m/s.

Try it (with your teacher, or a grown-up at home). Using a graph of your own walk, pick two points on a straight part. Read the distance and time at each, subtract to find the changes, and divide to find the speed. Compare it with your answer from the speed formula in section 11.1.

Exercise 11C  Speed from the gradient of a graph

1
FWhat is the formula for the gradient of a distance-time graph? Write the words.
2
FFrom 0 s to 4 s, Ali walks 20 m. What is the change in distance? Write the number of metres.
3
FFrom 0 s to 4 s, what is the change in time? Write the number of seconds.
4
FFrom 4 s to 6 s, what is the change in distance? Write the number of metres.
5
FWhat is the speed from 4 s to 6 s? Write the number of m/s.
6
PSFrom 0 s to 4 s, Ali's speed is 5 m/s. What is the distance he walks in that time? Write the number of metres.
7
PSFrom 6 s to 10 s, what is the change in time? Write the number of seconds.
8
PSFrom 6 s to 10 s, the change in distance is 30 m. What is the speed? Write the number of m/s.
9
PSA car goes from 0 m to 60 m in 6 s, at a steady speed. What is its speed? Write the number of m/s.
10
PSA pupil reads a straight line from 2 m at 1 s to 10 m at 3 s. What is the speed? Write the number of m/s.
11
PSBen says a graph line from 0 m to 20 m in 4 s has a speed of 4 m/s, because 4 is the time. Is Ben right? Write yes or no.
12
PSWorking scientifically: a pupil says the gradient of the flat section of a graph is 1, because the line is straight. Is this right? Write yes or no.
13
RChallenge: explain why the speed found from the gradient of a straight line is the same at any two points on that line. Write one sentence.
11.4

Mass and weight

Year 7
P2: mass and weight are different; mass is the amount of matter (kg), and weight is the gravitational force on it (N)
Video lesson: Mass and weightComing soon
Story. Sam says, “I weigh 50 kilograms.” His teacher says, “That is your mass. Your weight is a force, measured in newtons. They are related, but they are not the same thing.”

Mass is the amount of matter in an object. It is measured in kilograms (kg) with a balance, and it is the same everywhere.

Weight is the force of gravity pulling on an object. It is measured in newtons (N) with a newton meter, and it depends on where you are.

weight (N)the weight pulls the object down
An object on a table, with its weight pulling downwards.

The table compares mass and weight.

QuantityWhat it isUnitMeasured with
massthe amount of matter in an objectkilograms (kg)a balance
weightthe force of gravity on an objectnewtons (N)a newton meter

Key ideas

  • Mass is the amount of matter, in kilograms (kg); measured with a balance.
  • Weight is the force of gravity, in newtons (N); measured with a newton meter.
  • Mass is the same everywhere; weight changes with the strength of gravity.
  • A weight of 10 N means a gravity force of 10 newtons pulling the object down.
Worked example 11.4.1
What is the unit of mass? Write the unit.

Method. Recall the unit.

  1. Recall. Mass is measured in kilograms.
    kilograms
  2. Write the unit. The unit is kilograms, written kg.
    kg
  3. Write the answer.
    kg

Check. Mass is measured on a balance. ✓

Worked example 11.4.2
What is the unit of weight? Write the unit.

Method. Recall the unit.

  1. Recall. Weight is a force, measured in newtons.
    newtons
  2. Write the unit. The unit is newtons, written N.
    N
  3. Write the answer.
    N

Check. A newton meter measures weight. ✓

Worked example 11.4.3
Which instrument measures weight: a balance or a newton meter? Write the words.

Method. Recall the instrument.

  1. Recall. A balance measures mass, and a newton meter measures weight.
    newton meter
  2. Decide. So a newton meter measures weight.
    newton meter
  3. Write the answer.
    a newton meter

Check. Mass is measured with a balance. ✓

Watch out

Watch out: mass and weight are not the same. Mass is in kg, and weight is in N. A heavy object is one with a large weight, but in everyday speech the words are often mixed up.

Exam tip

Exam tip. Use kilograms for mass and newtons for weight. Do not write kg for weight.

Try it (with your teacher, or a grown-up at home). With a grown-up, hang a small bag of sugar on a newton meter, and read the weight in newtons. Then weigh the same bag on kitchen scales, in kg. Say which instrument measures mass and which measures weight.

Exercise 11D  Mass and weight

1
FWhat is the unit of mass? Write the unit.
2
FWhat is the unit of weight? Write the unit.
3
FWhich instrument measures mass? Write the word.
4
FWhich instrument measures weight? Write the words.
5
FIs the mass of an object the same on the Moon and on Earth? Write yes or no.
6
FIs the weight of an object the same on the Moon and on Earth? Write yes or no.
7
FWhich quantity is in kilograms: mass or weight? Write the word.
8
FWhich quantity is in newtons: mass or weight? Write the word.
9
PSSam says he weighs 50 kg. Is this a mass or a weight? Write the word: mass or weight.
10
PSA toy has a weight of 20 N on Earth. Is it the same mass on the Moon? Write yes or no.
11
PSAli says a balance measures weight in newtons. Is Ali right? Write yes or no.
12
PSWorking scientifically: a pupil says that weight is the same as mass because both are measured with a balance. Is this right? Write yes or no.
13
RChallenge: explain why an astronaut's mass is the same on Earth and on the Moon, but the weight is less on the Moon. Write one sentence.
11.5

Calculating weight: mass and gravity

Year 7
P2: weight = mass x gravitational field strength, measured in newtons; on Earth use 10 N/kg for calculations
Video lesson: Calculating weight: mass and gravityComing soon
Story. Ruby is building a model rocket for the school science fair. “My rocket has a mass of 2 kg, so what is its weight on Earth?” she asks. Her teacher says, “Multiply the mass by the gravitational field strength. On Earth, we use 10 newtons per kilogram.”

The weight of an object is the mass multiplied by the gravitational field strength, which is measured in newtons per kilogram (N/kg):

weight (N) = mass (kg) x gravitational field strength (N/kg)

On Earth, the gravitational field strength is about 10 N/kg, and we use 10 N/kg in calculations. On the Moon, it is about 1.6 N/kg, so the same mass has a smaller weight.

The table gives the mass of four objects, and their weight on Earth.

ObjectMass (kg)Weight on Earth (N), using 10 N/kg
a bag of sugar220
a school bag550
a small apple0.22.0
a bag of flour1.515.0

Key ideas

  • weight = mass x gravitational field strength
  • On Earth, use 10 N/kg for calculations.
  • Mass is in kg and weight is in N.
  • On the Moon the field strength is about 1.6 N/kg, so weight is less.
Worked example 11.5.1
A sugar bag has a mass of 2 kg. What is its weight on Earth? Write the number of newtons.

Method. Use weight = mass x 10 N/kg.

  1. Write the values. The mass is 2 kg, and the field strength is 10 N/kg.
    2 and 10
  2. Multiply. Weight = 2 x 10.
    2 x 10 = 20
  3. Write the answer.
    20 N

Check. 20 divided by 10 gives back the mass, 2 kg. ✓

Worked example 11.5.2
A school bag has a mass of 5 kg. What is its weight on Earth? Write the number of newtons.

Method. Use weight = mass x 10 N/kg.

  1. Write the values. The mass is 5 kg.
    5
  2. Multiply. Weight = 5 x 10 = 50.
    5 x 10 = 50
  3. Write the answer.
    50 N

Check. 50 divided by 10 is 5 kg. ✓

Worked example 11.5.3
A person has a mass of 60 kg. What is their weight on the Moon, where the field strength is 1.6 N/kg? Write the number of newtons.

Method. Use weight = mass x 1.6 N/kg.

  1. Write the values. The mass is 60 kg, and the field strength is 1.6 N/kg.
    60 and 1.6
  2. Multiply. Weight = 60 x 1.6 = 96.
    60 x 1.6 = 96
  3. Write the answer.
    96 N

Check. The same person weighs 600 N on Earth, so the Moon weight is much less. ✓

Watch out

Watch out: multiply mass by gravitational field strength. Do not divide. Check the answer has the unit N, not kg.

Exam tip

Exam tip. Write the formula, put in the mass in kg and the field strength in N/kg, then multiply. Give the unit N.

Try it (with your teacher, or a grown-up at home). With a grown-up, hang a bag of sugar on a newton meter and read its weight in N. Divide the weight in newtons by 10 N/kg to find the mass in kg, then compare it with the mass on the label, if there is one.

Exercise 11E  Calculating weight: mass and gravity

1
FWhat is the formula for weight? Write the words.
2
FWhat is the gravitational field strength on Earth, used in calculations? Write the number and unit.
3
FA bag of sugar has a mass of 2 kg. What is its weight on Earth? Write the number of newtons.
4
FA school bag has a mass of 5 kg. What is its weight on Earth? Write the number of newtons.
5
FA small apple has a mass of 0.2 kg. What is its weight on Earth? Write the number of newtons.
6
FA bag of flour has a mass of 1.5 kg. What is its weight on Earth? Write the number of newtons.
7
PSAn object has a mass of 4 kg. What is its weight on Earth? Write the number of newtons.
8
PSAn object has a weight of 30 N on Earth. What is its mass? Write the number of kilograms.
9
PSA person has a mass of 60 kg. What is their weight on Earth? Write the number of newtons.
10
PSThe same 60 kg person is on the Moon, where the field strength is 1.6 N/kg. What is the weight on the Moon? Write the number of newtons.
11
PSBen says a 10 kg object has a weight of 10 N on Earth. Is Ben right? Write yes or no.
12
PSWorking scientifically: a pupil says the weight of a 2 kg bag of sugar is 2 N on Earth. Explain the mistake. Write one sentence.
13
RChallenge: explain why the weight of a rocket would be different on the Moon, even though its mass is the same. Write one sentence.

Chapter summary

SkillMethod
Speedspeed = distance / time, in m/s.
Distance-time graphFlat means stopped. Steeper means faster. Time on the horizontal axis.
Gradientgradient = change in distance / change in time, which gives the speed of a straight section.
Mass and weightMass is in kg (balance). Weight is in N (newton meter). Mass is the same everywhere.
Weightweight = mass x gravitational field strength. On Earth use 10 N/kg.

Can you…?

  • I can calculate speed from distance and time, in m/s
  • I can read a distance-time graph, and say when an object is stopped or faster
  • I can find the speed of a straight section from its gradient
  • I can explain the difference between mass and weight, and their units
  • I can calculate weight from mass, using 10 N/kg on Earth

Key terms

speed
how far an object moves in each second, found by distance divided by time
distance-time graph
a graph of distance from the start against time
gradient
the steepness of a line; for a distance-time graph it gives the speed
mass
the amount of matter in an object, measured in kilograms
weight
the force of gravity on an object, measured in newtons
gravitational field strength
the force of gravity on each kilogram; 10 N/kg on Earth
newton (N)
the unit of force, used for weight

Exercise 11Z  Check-up

1
What is the formula for speed? Write the words.
2
A cyclist covers 300 m in 30 s. What is the speed? Write the number of m/s.
3
On a distance-time graph, what does a flat line mean? Write the word.
4
From 0 s to 4 s, the distance changes by 20 m. What is the speed? Write the number of m/s.
5
From 6 s to 10 s, the distance changes by 30 m. What is the speed? Write the number of m/s.
6
What is the unit of weight? Write the unit.
7
Which instrument measures weight? Write the words.
8
A bag of sugar has a mass of 2 kg. What is its weight on Earth? Write the number of newtons.
9
A person has a mass of 60 kg. What is their weight on the Moon, using 1.6 N/kg? Write the number of newtons.
10
Explain why mass is the same on the Moon and on Earth, but weight is not. Write one sentence.

Total 17 marks. Allow about 17 minutes.

Exercise 11X  Practice test questions

1
PSA runner covers 100 m in 25 s. What is the speed? Write the number of m/s.[2 marks]
2
FA distance-time graph is flat between 4 s and 6 s. What is the speed during that time? Write the number of m/s.[1 mark]
3
PSFrom 0 s to 10 s, a graph goes from 0 m to 50 m, in a straight line. What is the speed? Write the number of m/s.[2 marks]
4
FWrite the formula for weight. Write the words.[1 mark]
5
PSA school bag has a mass of 5 kg. What is its weight on Earth, using 10 N/kg? Write the number of newtons.[2 marks]
6
FName the unit of mass. Write the unit.[1 mark]
7
FAli says a balance measures weight. Is Ali right? Write yes or no.[1 mark]
8
PSAn object has a weight of 30 N on Earth. What is its mass, using 10 N/kg? Write the number of kilograms.[2 marks]
9
PSA cyclist covers 300 m in 30 s. Write the speed in m/s.[2 marks]
10
RExplain why a 60 kg person has a smaller weight on the Moon than on Earth. Write one sentence.[2 marks]
11
PSA toy car travels 12 m in 4 s. Write the speed in m/s.[1 mark]

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