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?
Method. Divide.
- Divide. Sixty shared into three equal parts gives 20 each.60 / 3 = 20
- Write the answer. 20
Check. Check: 20 x 3 = 60. ✓
Method. Recall the fact.
- Recall. One kilogram is one thousand grams.1 kg = 1000 g
- Write the answer. 1000
Check. So 2 kg is 2000 g. ✓
Method. Recall the unit.
- Recall. Short times in experiments are measured in seconds, written s.seconds
- Write the answer. seconds
Check. A stopwatch measures seconds. ✓
Method. Divide.
- Divide. Twelve shared into four equal parts gives 3 each.12 / 4 = 3
- Write the answer. 3
Check. Check: 3 x 4 = 12. ✓
Method. Multiply.
- Multiply. Four lots of 25 make 100.4 x 25 = 100
- Write the answer. 100
Check. Check: 100 divided by 4 is 25. ✓
Speed = distance divided by time
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 thing | Distance (m) | Time (s) | Speed (m/s) |
|---|---|---|---|
| a runner | 100 | 20 | 5 |
| a cyclist | 300 | 30 | 10 |
| a toy car | 12 | 4 | 3 |
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.
Method. Use speed = distance / time.
- Write the values. The distance is 100 m and the time is 20 s.100 and 20
- Divide. Speed = 100 / 20.100 / 20 = 5
- Write the answer. 5 m/s
Check. 5 x 20 = 100. ✓
Method. Use speed = distance / time.
- Write the values. The distance is 300 m and the time is 30 s.300 and 30
- Divide. Speed = 300 / 30.300 / 30 = 10
- Write the answer. 10 m/s
Check. 10 x 30 = 300. ✓
Method. The speed is the distance per second.
- Use the formula. Speed = 12 / 4.12 / 4 = 3
- Read the answer. So the car moves 3 m in each second, on average.3 m/s
- 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
Method. Recall the formula.
- Recall. Speed = distance / time.distance / time
- Write the answer. distance divided by time
Check. Speed is how far per second. ✓
Method. Think about the units.
- Think. Metres divided by seconds gives metres per second.metres per second
- Write. The unit is m/s.m/s
- Write the answer. m/s
Check. Read m/s as metres per second. ✓
Method. Divide the distance by the time.
- Divide. 100 divided by 20 is 5.100 / 20 = 5
- Write the answer. 5 m/s
Check. 5 x 20 = 100. ✓
Method. Divide the distance by the time.
- Divide. 300 divided by 30 is 10.300 / 30 = 10
- Write the answer. 10 m/s
Check. 10 x 30 = 300. ✓
Method. Divide the distance by the time.
- Divide. 12 divided by 4 is 3.12 / 4 = 3
- Write the answer. 3 m/s
Check. 3 x 4 = 12. ✓
Method. Divide the distance by the time.
- Divide. Speed = 2 / 4.2 / 4 = 0.5
- Write the answer. 0.5 m/s
Check. 0.5 x 4 = 2. ✓
Method. Divide the distance by the time.
- Divide. Speed = 40 / 80.40 / 80 = 0.5
- Write the answer. 0.5 m/s
Check. 0.5 x 80 = 40. ✓
Method. Divide the distance by the time.
- Divide. Speed = 50 / 10 = 5.50 / 10 = 5
- Write the answer. 5 m
Check. 5 x 10 = 50. ✓
Method. Divide the distance by the time.
- Divide. Speed = 240 / 20.240 / 20 = 12
- Write the answer. 12 m/s
Check. 12 x 20 = 240. ✓
Method. Use distance = speed x time.
- Multiply. Distance = 6 x 10.6 x 10 = 60
- Write the answer. 60 m
Check. 60 / 10 = 6. ✓
Method. Compare the speeds.
- Find the speeds. The runner is 5 m/s, and the cyclist is 10 m/s.5 and 10
- Decide. The cyclist is faster, so Ali is not right.no
- Write the answer. no
Check. Compare speeds, not distances. ✓
Method. Think about the formula.
- Think about the mistake. The pupil used the time as the speed.time as the speed
- Correct it. Speed = 100 / 20 = 5 m/s.5 m/s
- Write the answer. Accept any sentence that says 20 is the time, and the speed is distance divided by time, which is 5 m/s.
Check. Speed uses both distance and time. ✓
Method. Use distance = speed x time.
- Multiply. Distance = 15 x 8.15 x 8 = 120
- Check. Dividing back gives 120 / 8 = 15, which is the speed.120 / 8 = 15
- Write the answer. 120 m
Check. The formula can be rearranged. ✓
Distance-time graphs
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.
The table gives the distance from the start at each time.
| Time (s) | Distance from start (m) |
|---|---|
| 0 | 0 |
| 4 | 20 |
| 6 | 20 |
| 10 | 50 |
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.
Method. Read the graph at 5 seconds.
- Read the time. At 5 seconds, the line is flat, between 4 and 6 seconds.flat
- Read the distance. The distance is 20 m, the same as at 4 seconds.20
- Write the answer. 20 m
Check. Ali is stopped at this time. ✓
Method. Find the flat part of the line.
- Look for flat. The graph is flat between 4 s and 6 s.4 s and 6 s
- Write the times. So Ali was stopped from 4 s to 6 s.4 s and 6 s
- Write the answer. 4 s and 6 s
Check. The distance does not change while he is stopped. ✓
Method. Compare the slopes.
- Compare. From 0 to 4 s, Ali covers 20 m. From 6 to 10 s, he covers 30 m.20 m and 30 m
- Decide. The second part covers more distance in its time, so it is steeper.6 s to 10 s
- 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
Method. Recall the axes.
- Recall. Time goes along the horizontal axis.time
- Write the answer. time
Check. Distance goes up the vertical axis. ✓
Method. Recall the axes.
- Recall. Distance goes up the vertical axis.distance
- Write the answer. distance
Check. Time is on the horizontal axis. ✓
Method. Recall the meaning.
- Recall. A flat line means the distance does not change.does not change
- Decide. So the object is stopped.stopped
- Write the answer. stopped
Check. The distance stays the same. ✓
Method. Recall the meaning.
- Recall. A steeper line covers more distance in the same time.more distance
- Decide. So a steeper line means a faster speed.faster
- Write the answer. faster
Check. Steeper means faster. ✓
Method. Read the graph at 10 seconds.
- Read the graph. At 10 seconds, the line reaches 50 m.50
- Write the answer. 50 m
Check. The end of the walk. ✓
Method. Read the graph at 2 seconds.
- Read the graph. The line is halfway to 20 m at 2 seconds, so the distance is 10 m.10
- Write the answer. 10 m
Check. The line from 0 to 4 s is a straight slope. ✓
Method. Read the flat part.
- Read the flat part. The line is flat, so the distance stays at 20 m.stays at 20 m
- Decide. So the answer is no.no
- Write the answer. no
Check. Ali is stopped. ✓
Method. Compare the distances.
- Compare. From 0 to 4 s, Ali walks 20 m. From 6 to 10 s, he walks 30 m.20 m and 30 m
- Decide. So 6 s to 10 s is the longer walk.6 s to 10 s
- Write the answer. 6 s to 10 s
Check. Longest distance in the same or similar time. ✓
Method. Read the final distance.
- Read the end. At 10 seconds, he is 50 m from the start.50 m
- Write the answer. 50 m
Check. Ali did not walk back, so the distance from the start is his total walk. ✓
Method. Check the slope.
- Check. The distance never decreases, because every slope goes up or stays flat.never decreases
- Decide. So Ben is not right.no
- Write the answer. no
Check. Walking back would make the line go down. ✓
Method. Think about a fair test.
- Think. Use the same distance, and time each walk with a stopwatch.same distance
- Compare. The walk that takes less time is faster, and has a steeper line.less time
- Write the answer. Accept any test that times two walks over the same distance, with a steeper line for the faster walk.
Check. Keep the distance fixed to compare speeds. ✓
Method. Think about the distance.
- Think about stopping. When stopped, the distance from the start stays the same.stays the same
- Think about walking back. Only walking back would make the distance decrease.walking back
- Write the answer. Accept any sentence that says the distance from the start stays the same when the object stops, and does not fall unless it walks back.
Check. Distance from the start can only fall if the object goes back. ✓
Speed from the gradient of a graph
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) |
|---|---|---|---|---|
| 0 | 4 | 20 | 4 | 5 |
| 4 | 6 | 0 | 2 | 0 |
| 6 | 10 | 30 | 4 | 7.5 |
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.
Method. Use gradient = change in distance / change in time.
- Find the change in distance. The change in distance is 20 - 0 = 20 m.20
- Find the change in time. The change in time is 4 - 0 = 4 s.4
- Divide. Gradient = 20 / 4 = 5, so the speed is 5 m/s.20 / 4 = 5
- Write the answer. 5 m/s
Check. 5 x 4 = 20. ✓
Method. Use gradient = change in distance / change in time.
- Find the change in distance. The change in distance is 50 - 20 = 30 m.30
- Find the change in time. The change in time is 10 - 6 = 4 s.4
- Divide. Gradient = 30 / 4 = 7.5, so the speed is 7.5 m/s.30 / 4 = 7.5
- Write the answer. 7.5 m/s
Check. 7.5 x 4 = 30. ✓
Method. The line is flat, so the change in distance is zero.
- Find the change in distance. The distance is 20 m at both times, so the change is 0.0
- Divide. Gradient = 0 / 2 = 0, so the speed is 0 m/s.0 / 2 = 0
- 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
Method. Recall the formula.
- Recall. Gradient = change in distance / change in time.change in distance
- Write the answer. change in distance divided by change in time
Check. The gradient is the speed. ✓
Method. Subtract the start from the end.
- Subtract. The change is 20 minus 0.20 - 0 = 20
- Write the answer. 20 m
Check. The start is 0 m. ✓
Method. Subtract the start from the end.
- Subtract. The change is 4 minus 0.4 - 0 = 4
- Write the answer. 4 s
Check. The walk took 4 seconds. ✓
Method. Subtract.
- Subtract. The distance is 20 m at both times, so the change is 20 minus 20.20 - 20 = 0
- Write the answer. 0 m
Check. Ali is stopped. ✓
Method. Divide the change in distance by the change in time.
- Divide. Speed = 0 / 2 = 0.0 / 2 = 0
- Write the answer. 0 m/s
Check. No movement means zero speed. ✓
Method. Use distance = speed x time.
- Multiply. Distance = 5 x 4.5 x 4 = 20
- Write the answer. 20 m
Check. 20 / 4 = 5, the speed. ✓
Method. Subtract.
- Subtract. The change is 10 minus 6.10 - 6 = 4
- Write the answer. 4 s
Check. 6 + 4 = 10. ✓
Method. Divide the change in distance by the change in time.
- Divide. Speed = 30 / 4, which is 7.5.30 / 4 = 7.5
- Write the answer. 7.5 m/s
Check. 7.5 x 4 = 30. ✓
Method. Divide the change in distance by the change in time.
- Divide. Speed = 60 / 6.60 / 6 = 10
- Write the answer. 10 m/s
Check. 10 x 6 = 60. ✓
Method. Find the changes, then divide.
- Change in distance. 10 - 2 = 8 m.8
- Change in time. 3 - 1 = 2 s.2
- Divide. Speed = 8 / 2 = 4.8 / 2 = 4
- Write the answer. 4 m/s
Check. 4 x 2 = 8. ✓
Method. Divide the distance by the time.
- Divide. Speed = 20 / 4 = 5.20 / 4 = 5
- Decide. The speed is 5 m/s, not 4, so Ben is not right.no
- Write the answer. no
Check. Use the change in distance, not the time. ✓
Method. Think about a flat line.
- Think. A flat line has no change in distance, so the gradient is zero.zero
- Decide. So the gradient is not 1, and the answer is no.no
- Write the answer. no
Check. A flat line has zero gradient. ✓
Method. Think about the straight line.
- Think about the line. A straight line has the same slope all along it.same slope
- Think about the speed. So the change in distance per second is the same everywhere, meaning a steady speed.steady speed
- Write the answer. Accept any sentence that says a straight line has a constant gradient, so the change in distance per second is the same everywhere on it.
Check. A steady speed is a straight line. ✓
Mass and weight
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.
The table compares mass and weight.
| Quantity | What it is | Unit | Measured with |
|---|---|---|---|
| mass | the amount of matter in an object | kilograms (kg) | a balance |
| weight | the force of gravity on an object | newtons (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.
Method. Recall the unit.
- Recall. Mass is measured in kilograms.kilograms
- Write the unit. The unit is kilograms, written kg.kg
- Write the answer. kg
Check. Mass is measured on a balance. ✓
Method. Recall the unit.
- Recall. Weight is a force, measured in newtons.newtons
- Write the unit. The unit is newtons, written N.N
- Write the answer. N
Check. A newton meter measures weight. ✓
Method. Recall the instrument.
- Recall. A balance measures mass, and a newton meter measures weight.newton meter
- Decide. So a newton meter measures weight.newton meter
- 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
Method. Recall the unit.
- Recall. Mass is measured in kilograms, written kg.kg
- Write the answer. kg
Check. Mass is the amount of matter. ✓
Method. Recall the unit.
- Recall. Weight is a force, in newtons, written N.N
- Write the answer. N
Check. Weight is a force. ✓
Method. Recall the instrument.
- Recall. A balance measures mass.balance
- Write the answer. balance
Check. A newton meter measures weight. ✓
Method. Recall the instrument.
- Recall. A newton meter measures the force of weight.newton meter
- Write the answer. newton meter
Check. Weight is measured in newtons. ✓
Method. Think about mass.
- Think. Mass is the amount of matter, which does not change with place.does not change
- Decide. So the mass is the same, and the answer is yes.yes
- Write the answer. yes
Check. Only the weight changes with gravity. ✓
Method. Think about weight.
- Think. Weight depends on the strength of gravity, which is weaker on the Moon.weaker
- Decide. So the weight is different, and the answer is no.no
- Write the answer. no
Check. Weight changes with gravity. ✓
Method. Recall the units.
- Recall. Mass is measured in kilograms.kilograms
- Decide. So mass is in kilograms.mass
- Write the answer. mass
Check. Weight is in newtons. ✓
Method. Recall the units.
- Recall. Weight is measured in newtons.newtons
- Decide. So weight is in newtons.weight
- Write the answer. weight
Check. Newtons measure force. ✓
Method. Check the unit.
- Check. The unit kg is for mass.kg
- Decide. So it is a mass, and the answer is mass.mass
- Write the answer. mass
Check. A weight would be given in N. ✓
Method. Think about mass.
- Think. The mass does not change, even though the weight does.mass does not change
- Decide. So the mass is the same on the Moon, and the answer is yes.yes
- Write the answer. yes
Check. Mass stays constant. ✓
Method. Check the instrument.
- Check. A balance measures mass, in kilograms.mass
- Decide. So Ali is not right.no
- Write the answer. no
Check. Use a newton meter for weight. ✓
Method. Check the two quantities.
- Check. Mass is measured with a balance; weight is a force, measured with a newton meter.newton meter
- Decide. So weight is not the same as mass, and the answer is no.no
- Write the answer. no
Check. Mass and weight are different quantities. ✓
Method. Think about each quantity.
- Think about mass. Mass is the amount of matter, which stays the same.stays the same
- Think about weight. Weight is the force of gravity, which is weaker on the Moon.weaker
- Write the answer. Accept any sentence that says mass is the amount of matter, which does not change, but weight is the gravity force, which is weaker on the Moon.
Check. Mass and weight respond differently to gravity. ✓
Calculating weight: mass and gravity
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.
| Object | Mass (kg) | Weight on Earth (N), using 10 N/kg |
|---|---|---|
| a bag of sugar | 2 | 20 |
| a school bag | 5 | 50 |
| a small apple | 0.2 | 2.0 |
| a bag of flour | 1.5 | 15.0 |
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.
Method. Use weight = mass x 10 N/kg.
- Write the values. The mass is 2 kg, and the field strength is 10 N/kg.2 and 10
- Multiply. Weight = 2 x 10.2 x 10 = 20
- Write the answer. 20 N
Check. 20 divided by 10 gives back the mass, 2 kg. ✓
Method. Use weight = mass x 10 N/kg.
- Write the values. The mass is 5 kg.5
- Multiply. Weight = 5 x 10 = 50.5 x 10 = 50
- Write the answer. 50 N
Check. 50 divided by 10 is 5 kg. ✓
Method. Use weight = mass x 1.6 N/kg.
- Write the values. The mass is 60 kg, and the field strength is 1.6 N/kg.60 and 1.6
- Multiply. Weight = 60 x 1.6 = 96.60 x 1.6 = 96
- 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
Method. Recall the formula.
- Recall. Weight = mass x gravitational field strength.mass x gravitational field strength
- Write the answer. mass multiplied by gravitational field strength
Check. The unit of weight is N. ✓
Method. Recall the value.
- Recall. On Earth we use 10 N/kg in calculations.10 N/kg
- Write the answer. 10 N/kg
Check. This is a simple value for calculations. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 2 x 10.2 x 10 = 20
- Write the answer. 20 N
Check. 20 divided by 10 is 2 kg. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 5 x 10 = 50.5 x 10 = 50
- Write the answer. 50 N
Check. 50 divided by 10 is 5 kg. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 0.2 x 10 = 2.0.2 x 10 = 2
- Write the answer. 2 N
Check. 2 divided by 10 is 0.2 kg. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 1.5 x 10 = 15.1.5 x 10 = 15
- Write the answer. 15 N
Check. 15 divided by 10 is 1.5 kg. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 4 x 10 = 40.4 x 10 = 40
- Write the answer. 40 N
Check. 40 divided by 10 is 4 kg. ✓
Method. Divide the weight by 10 N/kg.
- Divide. Mass = 30 / 10 = 3.30 / 10 = 3
- Write the answer. 3 kg
Check. 3 x 10 = 30. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 60 x 10 = 600.60 x 10 = 600
- Write the answer. 600 N
Check. 600 divided by 10 is 60 kg. ✓
Method. Multiply the mass by 1.6 N/kg.
- Multiply. Weight = 60 x 1.6 = 96.60 x 1.6 = 96
- Write the answer. 96 N
Check. The weight is less on the Moon. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 10 x 10 = 100 N.10 x 10 = 100
- Decide. So the weight is 100 N, not 10 N, and Ben is not right.no
- Write the answer. no
Check. Remember to multiply. ✓
Method. Think about the formula.
- Think about the formula. Weight is mass multiplied by 10 N/kg.multiplied
- Correct it. So the weight is 2 x 10 = 20 N.20 N
- Write the answer. Accept any sentence that says the pupil forgot to multiply by 10 N/kg; the weight is 2 x 10 = 20 N.
Check. Check the formula before you multiply. ✓
Method. Think about the formula.
- Think about the mass. The mass is the same wherever the rocket is.same
- Think about the field strength. The Moon has a smaller field strength, so the weight is smaller.smaller
- Write the answer. Accept any sentence that says the field strength on the Moon is smaller, so the same mass has a smaller weight.
Check. Weight depends on the field strength. ✓
Chapter summary
| Skill | Method |
|---|---|
| Speed | speed = distance / time, in m/s. |
| Distance-time graph | Flat means stopped. Steeper means faster. Time on the horizontal axis. |
| Gradient | gradient = change in distance / change in time, which gives the speed of a straight section. |
| Mass and weight | Mass is in kg (balance). Weight is in N (newton meter). Mass is the same everywhere. |
| Weight | weight = 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
Method. Recall the formula.
- Recall. Speed = distance / time.distance / time
- Write the answer. distance divided by time
Check. Speed is distance per second. ✓
Method. Divide the distance by the time.
- Divide. Speed = 300 / 30 = 10.300 / 30 = 10
- Write the answer. 10 m/s
Check. 10 x 30 = 300. ✓
Method. Recall the meaning.
- Recall. A flat line means the distance does not change, so the object is stopped.stopped
- Write the answer. stopped
Check. The distance stays the same. ✓
Method. Divide the change in distance by the change in time.
- Divide. Speed = 20 / 4 = 5.20 / 4 = 5
- Write the answer. 5 m/s
Check. 5 x 4 = 20. ✓
Method. Divide the change in distance by the change in time.
- Divide. Speed = 30 / 4 = 7.5.30 / 4 = 7.5
- Write the answer. 7.5 m/s
Check. 7.5 x 4 = 30. ✓
Method. Recall the unit.
- Recall. Weight is measured in newtons, written N.N
- Write the answer. N
Check. Mass is in kg. ✓
Method. Recall the instrument.
- Recall. A newton meter measures weight.newton meter
- Write the answer. newton meter
Check. A balance measures mass. ✓
Method. Multiply by 10 N/kg.
- Multiply. Weight = 2 x 10 = 20.2 x 10 = 20
- Write the answer. 20 N
Check. 20 divided by 10 is 2 kg. ✓
Method. Multiply by 1.6 N/kg.
- Multiply. Weight = 60 x 1.6 = 96.60 x 1.6 = 96
- Write the answer. 96 N
Check. Weight is less on the Moon. ✓
Method. Think about each quantity.
- Think about mass. Mass does not change with place.does not change
- Think about weight. Weight depends on gravity, which is weaker on the Moon.weaker
- Write the answer. Accept any sentence that says mass is the amount of matter, which does not change, but weight depends on the strength of gravity.
Check. Mass and weight are different. ✓
Total 17 marks. Allow about 17 minutes.
Exercise 11X Practice test questions
Method. Divide the distance by the time.
- Divide. Speed = 100 / 25 = 4.100 / 25 = 4
- Write the answer. 4 m/s
Check. 4 x 25 = 100. ✓
Method. Think about a flat line.
- Think. A flat line means no change in distance, so the speed is zero.zero
- Write the answer. 0 m/s
Check. A stopped object has zero speed. ✓
Method. Divide the change in distance by the change in time.
- Divide. Speed = 50 / 10 = 5.50 / 10 = 5
- Write the answer. 5 m/s
Check. 5 x 10 = 50. ✓
Method. Recall the formula.
- Recall. Weight = mass x gravitational field strength.mass x gravitational field strength
- Write the answer. mass x gravitational field strength
Check. The unit of weight is N. ✓
Method. Multiply the mass by 10 N/kg.
- Multiply. Weight = 5 x 10 = 50.5 x 10 = 50
- Write the answer. 50 N
Check. 50 divided by 10 is 5 kg. ✓
Method. Recall the unit.
- Recall. Mass is measured in kilograms.kilograms
- Write the answer. kg
Check. Weight is measured in newtons. ✓
Method. Check the instrument.
- Check. A balance measures mass; a newton meter measures weight.newton meter
- Write the answer. no
Check. Use a newton meter for weight. ✓
Method. Divide the weight by 10 N/kg.
- Divide. Mass = 30 / 10 = 3.30 / 10 = 3
- Write the answer. 3 kg
Check. 3 x 10 = 30. ✓
Method. Divide the distance by the time.
- Divide. Speed = 300 / 30 = 10.300 / 30 = 10
- Write the answer. 10 m/s
Check. 10 x 30 = 300. ✓
Method. Think about gravity.
- Think about the mass. The mass of 60 kg is the same on the Moon.same
- Think about the weight. The Moon has a weaker field strength, so the weight is smaller.weaker
- Write the answer. Accept any sentence that says the Moon has a smaller gravitational field strength, so the same mass has a smaller weight.
Check. Weight depends on the field strength. ✓
Method. Divide the distance by the time.
- Divide. Speed = 12 / 4 = 3.12 / 4 = 3
- Write the answer. 3 m/s
Check. 3 x 4 = 12. ✓