Speed and motion graphs

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教育者の方へ： Speed and motion graphs（MYP Physics、Year 1）向けのすぐ使えるレッスンスライド, 復習ノート — レッスンで使うか、学習者がライブゲームとして遊ぶインタラクティブなクラス活動としてトピックを実施できます。

レッスンノート

Big idea: describing how things move

Big idea. Key concept: Change. Motion is a change of position over time, and we can describe it with numbers and graphs.
Related concept: Movement. Physicists describe movement using distance, time and speed.
Global context: Orientation in space and time. Knowing where things are and how fast they move lets us plan journeys, from walking to school to launching a satellite.
Distance is how far an object travels along its path. It is measured in metres (m) or kilometres (km). 1 km = 1000 m.
Time is how long the movement takes. It is measured in seconds (s), minutes (min) or hours (h).
If you walk from school to the shop along a winding path, the distance you travel is the length of the winding path, which is longer than the straight line between them.

Distance travelled along a winding path

Speed = distance / time

Speed tells us how far an object travels in each unit of time.
The equation is speed = distance ÷ time.
If a runner covers 100 m in 20 s, the speed is 100 m ÷ 20 s = 5 m/s. This means the runner travels 5 metres every second.
Rearranged, distance = speed × time and time = distance ÷ speed.
A walker moving at 4 m/s for 30 s travels 4 m/s × 30 s = 120 m. A person walking 600 m at 1.5 m/s takes 600 m ÷ 1.5 m/s = 400 s.
Typical speeds are about 1.5 m/s for walking, about 5 to 6 m/s for cycling and about 30 m/s for a car on a motorway.

A walker and a bee at different speeds

Units and average speed

Speed is measured in metres per second (m/s) or kilometres per hour (km/h). Always write the unit with your answer.
To change m/s into km/h, multiply by 3.6. To change km/h into m/s, divide by 3.6. So 20 m/s = 72 km/h, and 36 km/h = 10 m/s.
Before you calculate, make sure distance and time use matching units. 45 minutes is 0.75 hours, because 45 ÷ 60 = 0.75.
Real journeys have stops and changes of speed. Average speed = total distance ÷ total time.
Example: a ride covers 9 km in 50 minutes. 50 min = 50 ÷ 60 h = 0.83 h, so the average speed is 9 km ÷ 0.83 h = about 10.8 km/h.
A car's speedometer shows the speed at one moment. The average speed over a whole journey is usually lower than the highest speed because of stops and slow sections.

Distance-time graphs

A distance-time graph shows how far an object has travelled as time goes on. Time is on the horizontal axis and distance is on the vertical axis.
A flat, horizontal line means the distance is not changing, so the object is stationary.
A straight line sloping upwards means the object is moving at a constant speed.
A steeper line means a faster speed, because more distance is covered in the same time.
A line that curves upwards and gets steeper means the object is speeding up.
The graph for the journey in the picture has three sections: moving (A), stopped (B) and moving faster (C).

A journey with a moving, a stopped and a faster section

Gradient and speed

The gradient (slope) of a distance-time graph tells you the speed.
Gradient = change in distance ÷ change in time. On a graph, this is the rise divided by the run.
Example: an object is 8 m from the start at 4 s and 26 m from the start at 10 s. The change in distance is 26 - 8 = 18 m and the change in time is 10 - 4 = 6 s. The speed is 18 m ÷ 6 s = 3 m/s.
To find the speed from a graph, draw a large triangle on the straight part of the line, read the rise and run, and divide. A large triangle gives a more accurate answer.
You can also read distances straight off the graph, such as how far the object has gone after 10 s.
To compare two objects, plot both on the same axes. The one with the steeper line is faster.

Finding speed from the gradient of a graph

Think like a scientist: timing a trolley

Question: does the height of a ramp change how fast a trolley travels along a bench?
Mark a start line and a finish line 2.0 m apart. Release the trolley, start a stopwatch as it passes the start and stop it as it crosses the finish. Use speed = distance ÷ time.
The independent variable is the ramp height. The dependent variable is the speed. Control variables include the same trolley, the same ramp surface and the same start and finish lines.
A hand-held stopwatch has reaction-time error at the start and the finish. Using a longer distance, or light gates, reduces its effect.
To make results more reliable, repeat each timing at least three times and use the mean. For example, times of 4.2 s, 4.0 s and 4.4 s have a mean of 4.2 s, giving a speed of 2.0 m ÷ 4.2 s = about 0.48 m/s.
Inquiry task: plan a fair test to compare how fast two people walk 20 m. List your variables, say what you will measure and how you will reduce timing errors, and say how you will decide who is faster.

スライド

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練習問題

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1.Which is the correct equation for speed?
Easy
- ASpeed = distance ÷ time
- BSpeed = distance × time
- CSpeed = time ÷ distance
- DSpeed = distance + time
2.Which of these is a unit of speed?
Easy
- AKilogram (kg)
- BNewton (N)
- CSquare metre (m²)
- DMetre per second (m/s)
3.What does a horizontal line on a distance-time graph show?
Easy
- AThe object is speeding up
- BThe object is moving at a constant speed
- CThe object is stationary
- DThe object is going backwards
4.Which quantity is usually plotted on the horizontal axis of a distance-time graph?
Easy
- ATime
- BSpeed
- CDistance
- DMass
5.Which of these moves with the greatest speed?
Easy
- AA walker at 1.5 m/s
- BA runner at 4 m/s
- CA cyclist at 6 m/s
- DA person on a slow stroll at 0.8 m/s
6.How do you change a speed in m/s into a speed in km/h?
Medium
- ADivide by 3.6
- BDivide by 60
- CMultiply by 3.6
- DMultiply by 1000
7.Two objects are plotted on the same distance-time graph. Line X is steeper than line Y. What does this tell you?
Medium
- AY is faster than X
- BX is faster than Y
- CX and Y are both stationary
- DX and Y have the same speed
8.How can you find the speed from a straight line on a distance-time graph?
Medium
- ARead the highest distance on the graph
- BFind the area under the line
- CRead the time at the end of the line
- DDivide the change in distance by the change in time

もっと問題

9.Which of these describes average speed?
Medium
- AThe total distance divided by the total time
- BThe speed at the very start of the journey
- CThe fastest speed reached during the journey
- DThe speed shown on the speedometer at one moment
10.
The table shows the distance of an object from its start, in one experiment.
Time (s) Distance (m)
0 0
2 6
4 12
6 12
8 12
What is the object doing between 4 s and 8 s?
Medium
- AMoving at a constant speed of 3 m/s
- BStationary
- CSlowing down
- DSpeeding up
11.
The table shows the distance of a toy car from its start.
Time (s) Distance (m)
0 0
1 3
2 6
3 9
4 12
Which description of the motion is correct?
Medium
- AIt is stationary
- BIt is speeding up
- CIt moves at a constant speed of 12 m/s
- DIt moves at a constant speed of 3 m/s
12.
Three runners took part in a race.
Runner Distance (m) Time (s)
P 100 20
Q 200 50
R 60 10
Which runner had the greatest average speed?
Medium
- ARunner P
- BRunner Q
- CRunner R
- DThey all had the same speed
13.What is the difference between the speed shown on a car's speedometer and the car's average speed for a journey?
Medium
- AThere is no difference
- BThe speedometer shows the speed at that moment; the average speed covers the whole journey
- CThe speedometer shows the average speed
- DThe average speed is always the highest speed reached
14.A student looks at a distance-time graph. A section is flat. She says that the object is moving very slowly. Is she right?
Medium
- AYes, because the graph is near the bottom
- BYes, because time is still passing
- CNo, because the object is stationary
- DNo, because the object is moving at its fastest
15.On a distance-time graph, a line starts flat and then curves upwards, getting steeper. What does this show?
Hard
- AThe object is slowing down
- BThe object is stationary
- CThe object is going backwards
- DThe object is speeding up
16.
The table shows a cycle ride in one experiment.
Time (min) Distance (km)
0 0
10 2
20 4
30 4
40 4
50 9
In which 10-minute interval was the cyclist's speed greatest?
Hard
- A0 to 10 minutes
- B10 to 20 minutes
- C20 to 30 minutes
- D40 to 50 minutes
17.A cyclist travels 18 km in 45 minutes. Which is a correct way to find her average speed in km/h?
Hard
- A18 ÷ 45
- B18 ÷ 0.75
- C18 × 45
- D45 ÷ 18
18.A student times a trolley on a bench once with a hand-held stopwatch. Which change would make her speed result more reliable?
Hard
- AUse a different trolley every time
- BTime it once but more carefully
- CRepeat the timing several times and find the mean
- DMeasure the distance in kilometres
19.A student wants to find out whether the height of a ramp changes the speed of a trolley. What is the independent variable?
Medium
- AThe speed of the trolley
- BThe time on the stopwatch
- CThe length of the bench
- DThe height of the ramp
20.A student times a toy car over a 2 m track with a hand-held stopwatch and gets a speed that varies a lot between trials. What is the most likely cause?
Hard
- AReaction time when starting and stopping the stopwatch
- BThe track being measured in metres
- CGravity changing between trials
- DUsing the equation speed = distance ÷ time
21.Which equation can be used to find the distance travelled?
Easy
- ADistance = speed × time
- BDistance = speed ÷ time
- CDistance = time ÷ speed
- DDistance = speed + time
22.How many metres are there in 1 kilometre?
Easy
- A10
- B100
- C1000
- D10 000
23.Which of these are units of speed? (select all that apply)
Easy
- AMetres per second (m/s)
- BKilometres per hour (km/h)
- CMiles per hour
- DKilogram (kg)
- ENewton (N)
24.Which of these can you work out from a distance-time graph? (select all that apply)
Medium
- AHow far the object has travelled at a given time
- BWhen the object was stationary
- CThe speed, from the gradient
- DThe mass of the object
25.Which of these would make a trolley timing experiment more reliable? (select all that apply)
Medium
- ARepeat the timing three times and find the mean
- BUse the same start and finish lines each time
- CStart the stopwatch at a different moment each time
- DStop timing before the trolley reaches the finish line
26.Which of these are the same speed as 10 m/s? (select all that apply)
Hard
- A36 km/h
- B600 m in 1 minute
- C100 m in 10 s
- D1000 m in 10 s
27.Speed tells us how far an object travels in each unit of time.
Easy
True or false?
28.A horizontal line on a distance-time graph shows an object moving at a constant speed.
Easy
True or false?
29.A speed of 1 km/h is faster than a speed of 1 m/s.
Medium
True or false?
30.The steeper the line on a distance-time graph, the greater the speed.
Medium
True or false?
31.The line on a graph of distance travelled against time can slope downwards.
Hard
True or false?
32.Average speed is found by dividing the total distance by the total time.
Medium
True or false?
33.Match each quantity to a unit that is used to measure it.
Easy
- Distance in a race
- Time in a race
- Speed in a race
- Distance on a road trip
- Metre (m)
- Second (s)
- Metre per second (m/s)
- Kilometre (km)
34.Match each part of a distance-time graph to what it shows.
Medium
- A horizontal line
- A straight line sloping upwards
- A steeper straight line
- A line that curves upwards and gets steeper
- Stationary
- Constant speed
- A faster constant speed
- Speeding up
35.Match each speed in metres per second to the same speed in kilometres per hour.
Medium
- 5 m/s
- 10 m/s
- 20 m/s
- 30 m/s
- 18 km/h
- 36 km/h
- 72 km/h
- 108 km/h
36.Put the steps for finding the speed of a trolley in a sensible order.
Medium
- Release the trolley and start the stopwatch
- Use the mean time to calculate speed = distance ÷ time
- Mark a start line and a finish line a measured distance apart
- Stop the stopwatch as the trolley crosses the finish line
- Repeat several times and find the mean time
37.Put these speeds in order, from slowest to fastest.
Medium
- 5 m/s
- 36 km/h
- 2 m/s
- 10 km/h
38.Complete the speed equation.
Easy
Speed = distance ÷ ____.
39.Complete the sentence about units.
Easy
The unit m/s stands for metres per ____.
40.Complete the sentence about graphs.
Medium
The gradient of a distance-time graph gives the ____ of the object.
41.Complete the sentence about changing units.
Medium
To change km/h into m/s, divide by ____.
42.Complete the sentence about whole journeys.
Medium
The total distance divided by the total time gives the ____ speed.
43.Complete the sentence about a flat section of a distance-time graph.
Hard
A flat horizontal section on a distance-time graph means the object is ____.
44.
The table shows the distance of an object from its start in one experiment.
Time (s) Distance (m)
0 0
10 20
20 40
30 40
40 100
Describe the motion of the object, using speeds in your answer.
Hard
45.Explain why the average speed of a car on a long journey is usually lower than the highest speed shown on its speedometer.
Medium
46.Describe how you would measure the speed of a trolley rolling along a bench, and how you would make your result more reliable.
Hard
47.A runner covers 100 m in 20 s. Calculate the speed of the runner in metres per second (m/s).
Easy
48.A walker moves at a steady speed of 4 m/s for 30 s. Calculate the distance travelled in metres (m).
Medium
49.A person walks 600 m at a speed of 1.5 m/s. Calculate the time taken in seconds (s).
Medium
50.A car travels at 72 km/h. Calculate its speed in metres per second (m/s).
Medium
51.A cycle ride covers 9 km in 50 minutes. Calculate the average speed in kilometres per hour (km/h). Give your answer to 1 decimal place.
Medium
52.
A distance-time graph has a straight line passing through two points.
Time (s) Distance (m)
4 8
10 26
Calculate the gradient of the line, which is the speed, in metres per second (m/s).
Medium
53.A coach travels 6 km at 12 km/h, then 6 km at 4 km/h. Calculate the average speed for the whole 12 km in kilometres per hour (km/h).
Hard
54.A student times a trolley over a 2.0 m track three times in one experiment: 4.2 s, 4.0 s and 4.4 s. Using the mean time, calculate the speed of the trolley in metres per second (m/s). Give your answer to 2 decimal places.
Hard

復習ノート

## Speed - **Speed = distance ÷ time**, so distance = speed × time and time = distance ÷ speed. - Units: **m/s** and **km/h**. 1 m/s = 3.6 km/h. - **Average speed = total distance ÷ total time**. ## Distance-time graphs - Time on the horizontal axis, distance on the vertical axis. - **Flat** line: stationary. **Straight sloping** line: constant speed. **Steeper**: faster. **Curving upwards**: speeding up. - **Gradient = change in distance ÷ change in time = speed**. ## Inquiry - Name the independent, dependent and control variables. - Time over a measured distance, repeat and use the mean. - Reaction time is a source of error with a hand-held stopwatch.

Distance: How far an object travels along its path, measured in metres or kilometres.
Time: How long a movement takes, measured in seconds, minutes or hours.
Speed: The distance an object travels in each unit of time.
Speed equation: Speed = distance ÷ time.
Metre per second (m/s): A unit of speed: the number of metres travelled each second.
Kilometre per hour (km/h): A unit of speed: the number of kilometres travelled each hour.
Average speed: The total distance divided by the total time of a journey.
Distance-time graph: A graph with time on the horizontal axis and distance on the vertical axis.
Stationary: Not moving, shown by a flat line on a distance-time graph.
Gradient: The slope of a line: change in distance divided by change in time, which is the speed.
Constant speed: Moving at the same speed all the time, shown by a straight sloping line.
Mean: The average of repeated measurements, found by adding them up and dividing by how many there are.

フラッシュカード

What is speed?

The distance travelled in each unit of time.

What is the speed equation?

Speed = distance ÷ time.

How do you find distance from speed and time?

Distance = speed × time.

How do you find time from distance and speed?

Time = distance ÷ speed.

What are two units of speed?

Metres per second (m/s) and kilometres per hour (km/h).

How do you change m/s into km/h?

Multiply by 3.6.

How do you change km/h into m/s?

Divide by 3.6.

What is 20 m/s in km/h?

72 km/h.

How many metres are in 1 km?

1000 m.

What is average speed?

Total distance divided by total time.

What does a flat line on a distance-time graph mean?

The object is stationary.

What does a straight sloping line on a distance-time graph mean?

The object moves at a constant speed.

What does a steeper line mean?

A greater speed.

How do you find speed from a distance-time graph?

Gradient = change in distance ÷ change in time.

What does a line that curves upwards and gets steeper show?

The object is speeding up.

Why do we repeat timing measurements?

To find a mean and make the result more reliable.

What error affects a hand-held stopwatch?

Reaction time when starting and stopping it.

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過去問

このトピックの過去問練習は近日公開。

近日公開

Time (s)	Distance (m)
0	0
2	6
4	12
6	12
8	12

Time (s)	Distance (m)
0	0
1	3
2	6
3	9
4	12

Runner	Distance (m)	Time (s)
P	100	20
Q	200	50
R	60	10

Time (min)	Distance (km)
0	0
10	2
20	4
30	4
40	4
50	9