Describing motion: distance, speed and acceleration

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レッスンノート

Position and Reference Points

To describe motion you first have to say where something is. Position is the location of an object measured from a reference point (also called the origin).
A position needs a number, a unit and a direction: "300 m from Kosma's house, towards the shop".
Along a straight line we choose one direction as positive; the opposite direction is then negative. In the figure the shop is at +300 m and the school is at -300 m.
Choosing a different reference point changes the position numbers, but not where anything really is or how far apart things are.

A number line with Kosma's house as the reference point: the school is at -300 m and the shop is at +300 m.

Distance and Displacement

Distance is the total length of the path travelled. It has no direction and is never negative.
Displacement is the change in position: the straight line from where you started to where you finished, with a direction. Displacement = final position - initial position.
In the figure the dashed winding path is the distance; the straight solid arrow from start to finish is the displacement.
If you walk 500 m to school and 500 m back home, your distance is 1000 m but your displacement is 0 m, because you ended where you started.
Both are measured in metres (m).

A winding dashed path from the school (start) to the shop (finish), with a straight solid arrow from start to finish.

Calculating Speed

Speed tells you how fast something moves: how much distance it covers in each unit of time.
average speed = distance / time, or v = d / t. With distance in metres and time in seconds, speed is in metres per second (m/s).
Example: a car travels between two poles 50 m apart in 2.5 s. Speed = 50 m / 2.5 s = 20 m/s.
Rearranged: distance = speed × time, and time = distance / speed. A car moving at 30 m/s covers 90 m in 3 s.
Make the units match before you divide: 1 km = 1000 m, 1 min = 60 s, 1 h = 3600 s. To change km/h into m/s, divide by 3.6 (72 km/h = 20 m/s).

Velocity: Speed with a Direction

Velocity is speed in a given direction. average velocity = displacement / time.
Velocity can be positive or negative: the sign shows the direction of travel along the line.
Example: James walks 2 km away from home in 30 minutes, then walks back in another 30 minutes. Distance = 4000 m and time = 3600 s, so his average speed is 4000 / 3600 = 1.1 m/s.
His displacement is 0 m, so his average velocity for the whole trip is 0 m/s, even though he never stopped walking.
Two cars can have the same speed but different velocities if they travel in different directions.

Acceleration

Acceleration is how quickly velocity changes. acceleration = change in velocity / time, or a = (final velocity - initial velocity) / t.
The unit is metres per second squared (m/s²): an acceleration of 2 m/s² means the velocity changes by 2 m/s every second.
Example: a car speeds up from 2 m/s to 10 m/s in 8 s. a = (10 - 2) / 8 = 1 m/s².
The same car then slows from 10 m/s to 4 m/s in 6 s. a = (4 - 10) / 6 = -1 m/s². The negative sign shows the acceleration points against the motion, so the car slows down.
When the velocity and acceleration arrows point the same way, the object speeds up. When they point opposite ways, it slows down.
An object moving at a constant velocity has zero acceleration, however fast it is going.

Three objects with velocity and acceleration arrows: arrows in the same direction (speeding up) and in opposite directions (slowing down).

Distance-Time Graphs

A distance-time graph puts time on the horizontal axis and distance on the vertical axis.
A flat (horizontal) line means the distance is not changing: the object is stationary.
A straight sloping line means the object covers equal distances in equal times: constant speed. A steeper line means a faster speed.
The slope of the line is the speed: slope = change in distance / change in time. In the figure the walker covers 100 m in 100 s, so the speed is 1 m/s.
A line that curves upwards, getting steeper, shows an object that is speeding up.

Distance-time graph for a walker: a straight line from 0 m at 0 s to 100 m at 100 s.

Speed-Time Graphs

A speed-time graph puts time on the horizontal axis and speed on the vertical axis.
A flat line means constant speed (not stationary, unless the line sits at 0 m/s).
A line sloping upwards means the object is speeding up; a line sloping downwards means it is slowing down.
The slope of the line is the acceleration: slope = change in speed / change in time. In the figure the cyclist goes from 0 to 12 m/s in 4 s, an acceleration of 3 m/s².
Read the axis titles first. The same flat line means "stopped" on a distance-time graph and "steady speed" on a speed-time graph.

Speed-time graph of a cyclist's ride in three parts.

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練習問題

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1.What is a reference point?
Easy
- AThe fastest point in a journey
- BA fixed place that positions are measured from
- CThe place where a journey ends
- DThe total length of a path
2.The figure shows seven buildings along a straight street. Each building is 100 m from the next. Kosma's house is the reference point and the direction towards the shop is positive. What is the position of Kevin's house?
Easy
- A-200 m
- B+500 m
- C+100 m
- D+200 m
3.The figure shows seven buildings along a straight street. Each building is 100 m from the next. Kosma's house is the reference point and the direction towards the shop is positive. What is the position of Komal's house?
Easy
- A-200 m
- B+200 m
- C-100 m
- D-300 m
4.Changing the reference point changes the actual distance between two houses.
Easy
True or false?
5.Complete the sentence.
Easy
A position is measured from a fixed place called the ____.
6.Which statement best describes displacement?
Easy
- AThe total length of the path travelled
- BThe straight-line change in position from start to finish, with a direction
- CHow fast an object is moving
- DThe time taken for a journey
7.Distance can be negative.
Easy
True or false?
8.It is possible to travel a distance of 1000 m and have a displacement of 0 m.
Easy
True or false?

もっと問題

9.The figure shows seven buildings along a straight street. Each building is 100 m from the next. Kogis walks from her house to Kosma's house and then on to the school. What distance does she walk?
Medium
10.The figure shows seven buildings along a straight street. Each building is 100 m from the next. Kholo walks from his house to Kosma's house and then to the school. What are his distance and displacement?
Medium
- ADistance 200 m, displacement 400 m towards the school
- BDistance 400 m, displacement 400 m towards the school
- CDistance 400 m, displacement 200 m towards the school
- DDistance 300 m, displacement 100 m towards the shop
11.The figure shows seven buildings along a straight street. Each building is 100 m from the next. Komal walks from his house to the shop and then to the school. What are his distance and displacement?
Medium
- ADistance 600 m, displacement 100 m towards the shop
- BDistance 1100 m, displacement 1100 m towards the school
- CDistance 500 m, displacement 600 m towards the school
- DDistance 1100 m, displacement 100 m towards the school
12.You stand at your front door. The street is 10 m away. You walk to the street and back to the front door. What distance have you walked?
Easy
13.You stand at your front door. The street is 10 m away. You walk to the street and back to the front door. What is your displacement?
Easy
14.Match each quantity to its description.
Medium
- Distance
- Displacement
- Speed
- Velocity
- Total length of the path travelled
- Change in position, with a direction
- Distance travelled per unit of time
- Displacement per unit of time
15.Which of these quantities include a direction? (select all that apply)
Medium
- ADistance
- BDisplacement
- CSpeed
- DVelocity
- EAcceleration
16.Which formula gives average speed?
Easy
- Atime / distance
- Bdistance / time
- Cdistance × time
- Dchange in velocity / time
17.Which of these is a unit of speed?
Easy
- Am/s²
- Bm
- Cm/s
- Ds
18.Bridget measures two poles beside a straight road to be 50 m apart. Most cars take 3 s to travel from one pole to the other. Calculate the average speed of these cars, to one decimal place.
Medium
19.Two poles on a straight road are 50 m apart. A taxi passes the first pole at t = 5.0 s and the second pole at t = 7.5 s. Calculate the average speed of the taxi.
Medium
20.Two poles on a straight road are 50 m apart. A taxi passes the first pole at t = 5.0 s and the second pole at t = 7.5 s. Calculate the average speed of the taxi.
Medium
- A6.7 m/s
- B10 m/s
- C20 m/s
- D125 m/s
21.Two poles on a straight road are 50 m apart. A bus passes one pole at t = 5.0 s and the other pole at t = 9.0 s. Calculate the average speed of the bus.
Medium
22.Bongani walks 100 m towards the shop, realises he has no money, and walks 100 m back home. The whole trip takes 2 minutes. Calculate his average speed in m/s, to one decimal place.
Medium
23.Bongani walks 100 m towards the shop and then 100 m back home. The whole trip takes 2 minutes. What is his average velocity for the whole trip?
Medium
- A0 m/s
- B1.7 m/s
- C0.8 m/s
- D100 m/s
24.A car travels at a steady 30 m/s. How far does it travel in 3 s?
Easy
25.A car travels at a steady 25 m/s. How long does it take to travel 100 m?
Medium
26.A car is travelling at 72 km/h. What is this speed in m/s?
Medium
- A259 m/s
- B72 m/s
- C1.2 m/s
- D20 m/s
27.A car drives north at 20 m/s and another drives south at 20 m/s. Which statement is correct?
Easy
- AThey have the same velocity but different speeds
- BThey have the same speed and the same velocity
- CThey have the same speed but different velocities
- DThey have different speeds and different velocities
28.Bridget measures the velocity of a car as -16.7 m/s. The minus sign means the car is slowing down.
Medium
True or false?
29.Explain how a person can walk for an hour at a steady pace and still have an average velocity of 0 m/s.
Medium
30.What does acceleration measure?
Easy
- AHow quickly velocity changes
- BHow far an object travels
- CHow quickly position changes
- DHow long a journey takes
31.An athlete speeds up from 0 m/s to 4 m/s in 2 s. Calculate the athlete's acceleration.
Medium
32.An aeroplane speeds up from 100 m/s to 200 m/s in 10 s. Calculate its acceleration.
Medium
33.An aeroplane speeds up from 200 m/s to 240 m/s in 20 s. Calculate its acceleration.
Medium
34.A car slows down from 10 m/s to 4 m/s in 6 s while moving in the positive direction. What is its acceleration?
Medium
- A-1 m/s²
- B+1 m/s²
- C-6 m/s²
- D+2.3 m/s²
35.An object's velocity arrow points right and its acceleration arrow points left. What is happening to the object?
Medium
- AIt is speeding up
- BIt is slowing down
- CIt is moving at a constant speed
- DIt is not moving
36.A car travelling in a straight line at a steady 30 m/s has zero acceleration.
Easy
True or false?
37.An acceleration of 3 m/s² means the object travels 3 m every second.
Medium
True or false?
38.Complete the sentence.
Easy
Acceleration is the change in ____ divided by the ____ taken.
39.Put the steps in order to calculate the acceleration of a bus that speeds up from 7 m/s to 15 m/s in 4 s.
Medium
- Write down the initial velocity, final velocity and time.
- Subtract the initial velocity from the final velocity.
- Divide the change in velocity by the time.
- Write the answer with the unit m/s².
40.A taxi pulls away from a stop sign. It has covered 2.5 m after 1 s, 10 m after 2 s, 22.5 m after 3 s and 40 m after 4 s. What does this show?
Medium
- AThe taxi is moving at a constant speed
- BThe taxi is accelerating, because it covers more distance each second
- CThe taxi is slowing down
- DThe taxi is stationary
41.The distance-time graph shows a journey in three parts. During which time interval is the object stationary?
Medium
- A0 s to 4 s
- B7 s to 9 s
- C4 s to 7 s
- DIt is never stationary
42.The distance-time graph shows a journey in three parts. Calculate the speed during the first 4 seconds.
Medium
43.The distance-time graph shows a journey in three parts. In which part is the object moving fastest?
Medium
- A0 s to 4 s
- B4 s to 7 s
- CThe speed is the same in every part
- D7 s to 9 s
44.The distance-time graph shows two runners, A and B. Which statement is correct?
Medium
- AA is faster, because A's line is steeper
- BB is faster, because B's line is lower
- CThey run at the same speed
- DBoth runners are stationary
45.The distance-time graph describes the motion of an athlete. Calculate the athlete's speed during the first 4 seconds.
Medium
46.The distance-time graph describes the motion of an athlete. What is the athlete's speed between 4 s and 7 s?
Medium
- A0 m/s
- B1 m/s
- C4 m/s
- D0.75 m/s
47.The speed-time graph shows a cyclist's ride in three parts. What is the cyclist doing between 4 s and 10 s?
Medium
- AStanding still
- BSpeeding up
- CSlowing down
- DRiding at a constant speed of 12 m/s
48.The speed-time graph shows a cyclist's ride in three parts. Calculate the acceleration during the first 4 seconds.
Medium
49.The speed-time graph shows a cyclist's ride in three parts. What is happening between 10 s and 13 s?
Medium
- AThe cyclist is riding back to the start
- BThe cyclist is speeding up
- CThe cyclist is slowing down
- DThe cyclist is riding at a constant speed
50.The speed-time graph shows a bus over 4 seconds. Calculate the acceleration of the bus.
Medium
51.On a distance-time graph, a steeper straight line shows a faster constant speed.
Easy
True or false?
52.A flat line on a speed-time graph always means the object has stopped.
Medium
True or false?
53.Match each graph feature to what it tells you about the motion.
Medium
- Flat line on a distance-time graph
- Straight sloping line on a distance-time graph
- Flat line on a speed-time graph
- Line sloping upwards on a speed-time graph
- Stationary
- Constant speed
- Constant speed, zero acceleration
- Speeding up
54.On a distance-time graph, what quantity does the slope of the line give?
Easy
55.A student says: "A flat line means the object has stopped, whichever motion graph you look at." Explain why this is not always true.
Medium

復習ノート

## Describing motion - **Position** is measured from a **reference point**; one direction along the line is positive and the other negative. - **Distance** is the total path length. **Displacement** is the straight-line change in position with a direction. A round trip has a displacement of 0 m. - **average speed = distance / time** and **average velocity = displacement / time**, both in m/s. Convert km/h to m/s by dividing by 3.6. - **acceleration = change in velocity / time**, in m/s². Same direction as the velocity: speeding up. Opposite direction: slowing down. Constant velocity: zero acceleration. - **Distance-time graph:** flat = stationary, straight slope = constant speed, steeper = faster, slope = speed. - **Speed-time graph:** flat = constant speed, sloping up = speeding up, sloping down = slowing down, slope = acceleration.

Reference point: The fixed place (origin) that positions are measured from.
Position: The location of an object measured from a reference point, with a direction.
Distance: The total length of the path travelled; no direction, never negative.
Displacement: The change in position from start to finish, with a direction.
Average speed: Distance travelled divided by the time taken (m/s).
Average velocity: Displacement divided by the time taken (m/s), with a direction.
Acceleration: Change in velocity divided by the time taken (m/s²).
Slope: The steepness of a graph line: change in the vertical quantity divided by change in the horizontal quantity.

フラッシュカード

What is a reference point?

A fixed place (the origin) that positions are measured from.

What is position?

Where an object is, measured from a reference point, with a direction (positive or negative).

What is distance?

The total length of the path travelled. It has no direction and is never negative.

What is displacement?

The change in position from start to finish, with a direction: final position - initial position.

You walk 500 m to school and 500 m home. Distance and displacement?

Distance = 1000 m. Displacement = 0 m.

How do you calculate average speed?

average speed = distance / time (v = d / t).

What is the unit of speed?

Metres per second (m/s).

How is velocity different from speed?

Velocity is speed in a given direction: displacement / time. It can be negative.

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

Divide by 3.6 (for example, 72 km/h = 20 m/s).

How do you calculate acceleration?

acceleration = change in velocity / time.

What is the unit of acceleration?

Metres per second squared (m/s²).

What does a negative acceleration mean for an object moving in the positive direction?

It is slowing down.

What is the acceleration of an object moving at constant velocity?

0 m/s².

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

The object is stationary.

What does the slope of a distance-time graph give?

The speed.

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

Constant speed (zero acceleration).

What does the slope of a speed-time graph give?

The acceleration.

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