Describing Motion

Describing Motion
Introduction to Kinematics
Stephen Taylor & Paul Wagenaar
Canadian Academy, Kobe
Draft Presentation – will be updated staylor@canacad.ac.jp

How do you know that something is moving?

Whee! By Todd Klassy, via the Physics Classroom Gallery
http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/

How do you know that something is moving?
Motion is change.
Mechanics is the Science of Motion.
Kinematics is the science of describing motion
using graphs, words, diagrams and calculations.

Our unit question:

“How can we describe change?”

Whee! By Todd Klassy, via the Physics Classroom Gallery
http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/

How can we describe movement?

Usain Bolt’s 100m world record (not his false start!)
http://www.youtube.com/watch?v=3nbjhpcZ9_g



Strobe diagrams can be used to measure distance / time:
Analyse this strobe diagram. What does it show? What are the dots?

0m 100m

Sketch a distance/ time graph for Bolt.


Strobe diagrams can be used to measure distance / time:
Analyse this strobe diagram. What does it show? What are the dots?

0m 100m

Describing Motion
Distance
- how far an object travels along a path.

Which object is 2m away from the juggler?

Juggler

Which object is 2m away from the juggler?

Juggler

Distance is not always enough!

How can someone run for 45 seconds but
go nowhere? (and they are not on a treadmill)


http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m12s

Sketch a distance/ time graph for Johnson.



Sketch a distance/ time graph for Johnson.

Sketch a displacement/ time graph for Johnson.

Distinguish
between distance
and displacement.

Describing Motion
Distance
- how far an object travels along a path.
Displacement
- the position of an object in reference to an origin or
to a previous position.

Scalars, such as distance, are non-directional measures
of movement.
Vectors, such as displacement, are directional.

Which might be more important to a pilot?

What are the coordinates of these objects?
Coordinates can be used to describe an objects position or displacement.

2mE, 1mN

origin

Pick a mystery object.
Describe the displacement to three other objects.
Can another group deduce the objects?

Example:

From (mystery object)
It is:
• 1mE, 1mS to the
______________________
• 4mS to the
______________________
• 2mS, 4mE to the
______________________


Example:

From (mystery object)
It is:
• 1mE, 1mS to the
Big Squirrel
• 4mS to the
Enthusiastic Runner
• 2mS, 4mE to the
Tiny Cyclist


Example:

From (Giant Acorn)
It is:
• 1mE, 1mS to the
Big Squirrel
• 4mS to the
Enthusiastic Runner
• 2mS, 4mE to the
Tiny Cyclist

The components (coordinates) of displacement tell us where the object has moved
to overall, but they do not necessarily tell us the path it has taken.

Which objects are:
• 2.1m away from the origin at 14oN of East?
• 5m away from the origin at 30oN of East?

Magnitude and Direction tell us the displacement in terms of
the most direct path.

N

E

origin

Magnitude and Direction can also be represented by directed
line segments (vector diagrams).

N

E

1m

The direction (angle relative to the
orientation) and magnitude (length of
the vector) are important.

Which objects lie closest to these vectors?
(directed line segments – hint, start at origin, length is important)
A
N

E

N B

E

N C

E

Three ways of describing displacement
Components (coordinates or directional descriptors)
- e.g. 3mE, 2mN of origin

Magnitude and Direction
- described, e.g. 2.1m 14oN of origin
A
Vectors (directed line segments)
- direction and magnitude are important N

E

Describing displacement

N
Components (coordinates or
directional descriptors)
- e.g. 3mE, 2mN of origin

- described, e.g. 2.1m 14oN of
origin

- direction and magnitude are
important

Ke$ha’s Day Out on Rokko Island N
1km
1. Wake up in the morning (11am) feeling like P Diddy.
2. Get a pedicure, 5kmE 2.5kmS of home.
3. Then hit the clothes store, 30oNorth of East 5km away.
4. Cruise along, top down, CD’s on. Along this vector (directed line segment) to club.
5. Club closes 1am. Walk home.
6. Arrive home 4am by most direct route.

Wake up feeling like P
Diddy
$

1km
1. Wake up in the morning (11am) feeling like P Diddy.
2. Get a pedicure, 5kmE 2.5kmS of home.
3. Then hit the clothes store, 30oNorth of East 5km away.
4. Cruise along, top down, CD’s on. Along this vector (directed line segment) to club.
5. Club closes 1am. Walk home.
6. Arrive home 4am by most direct route. Club

Diddy
$ Clothes

Pedicure

1km
1. Calculate:
a. Total distance b. Total displacement c. Average speed d. Average velocity

e. Average speed on the walk home. Club

Diddy
$ Clothes

2. Describe the displacement
of the pedicurist from her house using:
a. directed line segment Pedicure
b. direction and magnitude

Kinematics in Sport Criterion E: Processing Data

1. Pick a short clip of a sequence of
movements in a sport. It must be:
• In a defined area
(e.g. football field or floor gymnastics mat)
• Multi-directional (not just linear)
2. Map out the area using graph paper,
including scale and descriptor of direction
3. Analyse the video clip and try to plot the
position of the object (or person) at each
change in direction. Label clearly.
4. Describe the displacement of each move.

N Use each of these tools at least twice in
4 0 your descriptions of the movements.

Components
(coordinates or directional descriptors)
3
6 described, e.g. 2.1m 14oN of origin
scale

1 direction and magnitude
2
5

Walk This Way Using LoggerPro to generate distance/time graphs.

Challenge 1:
• Open the experiment “01b Graph Matching.cmbl”
• Give everyone a chance to move themselves to follow the line as closely as
possible. Make sure the motion sensor is aimed at the body the whole time.
• Save some good examples and share them with the group.

What does the line show?

resting

Fast constant motion

Slow constant motion

towards the sensor
away from the sensor


Challenge 1:
• Open the experiment “01b Graph Matching.cmbl”
• Give everyone a chance to move themselves to follow the line as closely as
possible. Make sure the motion sensor is aimed at the body the whole time.
• Save some good examples and share them with the group.

What does the line show?

resting
Slow constant motion
towards the sensor
Fast constant motion
away from the sensor resting

resting


Challenge 2:
• Open the experiment “01a Graph Matching.cmbl”
• Produce your own – differently-shaped - 10-second motion that includes all of the
following characteristics:
• Slow constant motion, fast constant motion and resting (constant zero motion)
• Motion towards and away from the sensor
• Acceleration
• Changes in motion

Save your graph and share it
with the group.

Label the parts of the graph and
add it to your word doc for
submission to Turnitin.

Speed or Velocity?
Speed is the rate of change of position of an object.

Over time How fast is it moving?
Speed is a scalar quantity.
e.g. m s-1
(metres per second)

Velocity is the rate of change of position of an
object – with direction.
How fast is it moving in that direction?
Velocity is a vector quantity.
e.g. m s-1 East
(metres per second to the East)

Calculating Speed & Velocity

Distance
Speed Or
Δd Displacement

v= Δt Time
Velocity

The delta symbol (Δ) is used
to represent “change in”

Calculating Speed
Δd
At what speed did the object move away from the sensor?
v= Δt

Δd
v=
Δt

Calculating Speed
Δd
v= Δt

Δd

Δt v=

Calculating Speed
Δd
v= Δt

Δd
2.5m – 1m = 1.5m

1.5m
Δt 3s – 1s = 2s
v= 2s

Calculating Speed
Δd
v= Δt

Δd
2.5m – 1m = 1.5m

v= 1.5m
= 0.75ms-1
Δt 3s – 1s = 2s 2s

Calculating Speed
Δd
v= Δt

Δd
2.5m – 1m = 1.5m
“per second”

v= 1.5m
= 0.75ms-1
Δt 3s – 1s = 2s 2s
(2d.p.)

Calculating Speed
Δd
At what speed did the object move toward the sensor?
v= Δt

Δd
v=
Δt

Calculating Speed
Δd
v= Δt

Δd

Δt

Δd
v=
Δt

Calculating Speed
Δd
v= Δt
Remember: speed is a
scalar, not a vector, so
direction is not important
Δd (don’t use negatives)
2.5m – 1.75m = 0.75m
Δt 7.5s – 6s = 1.5s

v= 0.75m
1.5s
= 0.5ms-1

Instantaneous Speed
Δd
Is the speed of an object at any given moment in time.
v= Δt

X
X
X X

X

Instantaneous Speed
Δd
Is the speed of an object at any given moment in time.
v= Δt

X
v = 0.00ms-1 X v = 0.5ms-1
X X
v = 0.75ms-1 v = 0.00ms-1
X
v = 0.00ms-1

Average Speed
Δd
Is the mean speed of an object over the whole journey.

“mean”
v= Δt

Every movement adds to
the total distance traveled
Δd + Δd

Δt = 10 seconds

v= 1.5m + 0.75m
10s
= 0.225ms-1

Calculating Velocity
Δd
At what velocity did the object move away from the sensor?
v= Δt

Δd
v=
Δt

Δd
v= Δt

Δd

Δt v=

Δd
v= Δt

Δd
2.5m – 1m = 1.5m

1.5m
Δt 3s – 1s = 2s
v= 2s

Δd
v= Δt

When the person moves away
from the sensor, distance and
Δd displacement are the same.

2.5m – 1m = 1.5m

v= 1.5m
= 0.75ms-1
Δt 3s – 1s = 2s 2s (away from sensor)

Δd
v= Δt

When the person moves toward
the sensor, displacement is lost. Δd
1.75m – 2.5m= -0.75m
Δt

v= 0.75m
= -0.5ms -1
1.5s (toward sensor)

Positives and Negatives in Velocity
Velocity is direction-dependent. It can have positive and negative values.
We can assign any one direction as being the positive.
In the ball-throw examples, the data-logger has assigned movement away from
the sensor (gaining displacement) as being the positive. Therefore movement
towards the sensor is negative velocity.
Identify which motions show positive, negative and zero velocity.

North is positive. East is positive. South is positive. N



+ve

zero
+ve

-ve

-ve



+ve +ve

+ve
zero
+ve -ve

-ve -ve

-ve
+ve



+ve +ve -ve

zero +ve zero
+ve -ve
-ve

-ve -ve +ve

-ve
+ve +ve

Instantaneous Velocity
Δd
Is the velocity of an object at any given moment in time.
v= Δt

X
X
X

X

Δd
v= Δt

X
v = 0.00ms-1 X
X
v = 0.75ms-1
X
v = 0.00ms-1

Δd
v= Δt

X
v = 0.00ms-1 X v = -0.5ms-1
X
v = 0.75ms-1 Velocity is a vector.
It is direction-specific.
This point moving closer to the
X origin can be negative.
v = 0.00ms-1

Average Velocity
Δd
Is the mean velocity of an object over the whole journey.

“mean”
v= Δt

v=

Average Velocity
Δd
Is the mean velocity of an object over the whole journey.

“mean”
v= Δt

v= 1.75m – 1.00m
= 0.075ms -1
10s
(away from sensor)

Δd

Δt = 10 seconds

Comparing Speed and Velocity
Δd
Mean speed is non-directional. ∆d = all distances
Mean velocity is directional. ∆d = total displacement v= Δt

v= 0.225ms -1
Mean speed

v= 0.075ms-1
(away from sensor)
Mean velocity

Calculating Speed & Velocity
Δd
Calculate the following in your write-ups.
v= Δt
Challenge A:
a) Your speed of movement away from the sensor
b) Your average velocity over the 10-second run

Challenge B:
a) Your instantaneous velocity at any single point of constant motion
b) b) Your average velocity over the 10-second run

Ball Challenge (coming up):
a) Maximum velocity of the ball when falling
b) Average velocity of the ball


Ball Challenge:
• Open the experiment “02 Ball.cmbl”
• Position the motion sensor on the floor or table, facing up.
• Hold the volleyball about 3m above the sensor
• Have someone ready to catch the ball before it hits the sensor.
• Start the sensor, drop and catch the ball. Do this a few times.
• Save and label the two graphs: distance/time and velocity/time.
• Use these in your write-up to explain what is meant by velocity.

Explain this!
Distance from sensor (m)

Velocity (ms-1)

Explain this!
Changing direction

Slowing Speeding up

Going upwards Falling
Speeding up
Resting
Caught

Velocity (ms-1)
Let go

Speeding up Slowing
Resting
Changing direction
Speeding up
(falling) Caught

Walk This Way Submitting your work

Lab report
• Assessed for Criterion E: Processing Data
• Complete all the work in the class period to avoid homework.
• Self-assess the rubric using a highlighter tool before submission.
• Submit to Turnitin.com
Pay attention to the task-
specific notes to make sure you
achieve a good grade

Work-done Wednesday
By the end of the lesson:
• Complete the Walk This Way lab and submit your work
• Self-assess using the highlight tool
• Check your graphs for:
• Titles, axes labeled, units, clear and sensible annotations
• Be sure that your explanations demonstrate your understanding of:
• The difference between distance and displacement
• Velocity
• Speed and velocity calculations

If you are done:
• Use the resources here to check your understanding:
• http://i-biology.net/myp/intro-physics/describing-motion/
• Find out more about acceleration
• Use graph paper to set your own questions on displacement, speed and velocity
• Review all of the language used so far. Can you use it confidently?

Calculating values on a curve
If we are calculating values of constant motion, life is easy. There is a straight line and
we can draw a simple distance-time triangle to calculate speed or velocity.

What about here?
X

Time (s)


What about here?
X
A triangle is not representative of the curve!

Time (s)


If we draw a tangent to the
curve at the point of interest
we can use the gradient of
the line to calculate the speed
or velocity of the object – at
that moment in time.

X

Time (s)


If we draw a tangent to the
curve at the point of interest
we can use the gradient of
the line to calculate the speed
or velocity of the object – at
that moment in time.

X
Now the triangle fits the point.

Time (s)


If we draw a tangent to the curve at
the point of interest we can use the line
to calculate the speed or velocity of the
object – at that moment in time.

X
Now the triangle fits the point.

Time (s)

Δd
v= = (0.6m – 0.25m)
(0.4s)
= 0.875ms-1
Δt

Warm-up questions
1. Your average speed on a 64m journey is 80kmh-1. How long does it take?

2. A duck is on a pond. It starts 8m from the North edge and and swims for 10
seconds. It finishes 2m North of the edge.
a. What was its velocity?

b. Draw a vector diagram to show its displacement.

Speed and Velocity Δd
v=
A ball is thrown up in the air and caught. Determine: Δt
a. The instantaneous velocity of the ball at points A and B
b. The average velocity of the ball.

2 B

A
1

0 0.5 1
Time (s)

Velocity and Vectors Δd
v=
Velocity is a vector – it has direction. Δt
We can use velocity vector diagrams to describe motion.
The lengths of the arrows are magnitude – a longer arrow means +
greater velocity and are to scale. The dots represent the object at
consistent points in time. The direction of the arrow is important.
Describe the motion in these velocity vector diagrams:

origin Positive velocity, increasing velocity.

+ origin

origin

origin +

Velocity and Vectors Δd
v=
Velocity is a vector – it has direction. Δt
We can use velocity vector diagrams to describe motion.
The lengths of the arrows are magnitude – a longer arrow means +
greater velocity and are to scale. The dots represent the object at

Positive velocity, decreasing velocity.

Negative velocity, increasing velocity.
consistent points in time. The direction of the arrow is important.
Describe the motion in these velocity vector diagrams:

origin Positive velocity, increasing velocity.

+ Negative velocity, increasing velocity. origin

origin
Object moves quickly
away from origin, slows,
origin Positive velocity, decreasing velocity. +
turns and speeds up on
return to origin.

The birds are angry that the pigs destroyed their
Velocity and Vectors nests – but luckily they have spotted a new nesting
site. However, short-winged and poorly adapted to
flight, they need to use a slingshot to get there.
Draw velocity vectors for each position of the angry bird to show its relative instantaneous
velocity. Use the first vector as a guide.
The flight takes 2.3s. Calculate:
• vertical displacement of the bird.
• average velocity (up) of the bird.
• average velocity (right) of the bird.
• average overall velocity
(include direction
and magnitude)

1.6m
55cm
7.5 m

Velocity and Vectors
Draw velocity vectors for each position of the angry bird to show
its relative instantaneous velocity. Use the first vector as a guide.

Draw velocity vectors for each position of the angry bird to show
its relative instantaneous velocity. Use the first vector as a guide.

Remember that velocity vectors represent velocity – not
distance. So it doesn’t matter if there is an object in the way
– the velocity is the same until the moment of impact.

Draw velocity vector diagrams for each of these karts.

10kmh-1 16kmh-1 8kmh-1 20kmh-1

Use the known vector as the scale.

A rugby ball is displaced according to the vector below, for 0.6 seconds.
Determine the velocity of the ball.

2m

30o

A rugby ball is displaced according to the vector below, for 0.6 seconds.
Determine the velocity of the ball.

Δd 10
v= Δt = 0.6 = 16.7ms-1
(30o up and forwards)

2m

30o

RIC Roll: Drive Safe 1 mile = 1.61km

What are the speed limits (kmh-1) where
you live or come from?

Why are they set to those values?

How is it enforced?
What are the penalties?

http://www.youtube.com/watch?v=L7fhzDUOsxI

Two basic methods are used to police
speeding on the roads:
- instantaneous velocity
- average velocity over a longer journey
As a group explain how they work and
discuss the pros and cons of each.
http://www.youtube.com/watch?v=Qm8yyl9ROEM

RIC Roll: Drive Safe Applying Science to Local Issues

Lots of children and senior citizens live in Rokko Island
City (RIC). As a group they are at greatest risk from
injuries due to speeding cars. They have been
complaining of a group of street-racers on the island who
they think are driving too fast.
Unfortunately budgets are tight and the police can only
take action if the community are able to give them good
information on the speed at which these racers are going.
The city council’s RIC Roll: Drive Safe project aims to
promote community participation in safe-speed road
behaviour. They need your input in designing the project. Rokko Island City (inside the green belt), via GoogleMaps

Your task:
80-minute project
• Develop a simple method for judging the speed
of a car as it passes anywhere within the green
• Group method
belt on the island. • Present at the end of class
• It must be cheap and effective. • 1 slide maximum
• It must be easily understood by kids and adults. • Outline method
• It cannot make use of any technology other than • Evaluate limitations
that which is available to most people.
• It must have a foundation in our unit.


Record and calculate the instantaneous speed of 5 cars passing the school.
How much variation is there within your group?
Car 1 2 3 4 5
Person A

Δd
Person B
Person C
Mean
Range
v= Δt

Limitations Effects on Results Solutions
Evaluate the reliability of
this method for
estimating speed of cars.


The local speed limit is 40kmh-1.
Δd
v=
If we adopt the method of putting markers at set
distances along each road, can you rearrange the

Δt equation so that local people can determine whether or
not a car is speeding – just by counting?


The local speed limit is 40kmh-1.
Δd
v=
If we adopt the method of putting markers at set
distances along each road, can you rearrange the

Δt equation so that local people can determine whether or
not a car is speeding – just by counting?

t.v = d Sampled distance (you decide)
This example: 50m

d
t=v =
50m
=
50m
=
50m
=
4.5s
40kmh-1 40 x 1000
( ) 11.1ms-1
3600


Now have a go using this free app:
http://itunes.apple.com/us/app/simple-radar-gun/id442734303?mt=8

Use the manual settings to enter your set distance.
Press to start, release to stop.

It is not really a radar gun, though it is a useful tool.

Can you explain exactly how it works?

Can you evaluate some limitations of the app?

Criterion A: One World
RIC Roll: Drive Safe Criterion B: Communication in Science
Lots of children and senior citizens live in Rokko Island City
(RIC). As a group they are at greatest risk from injuries due to
speeding cars. The city council’s RIC Roll: Drive Safe project
aims to promote community participation in safe-speed road
behaviour.
The most effective consultancy team’s project proposal will
be adopted.

Key to success in the project:
• a system which will allow all citizens to determine Rokko Island City (inside the green belt), via GoogleMaps
the speed of a car
• very low-budget but high-impact campaign

In your proposal presentation:
• Clearly define the problem in the context of community safety.
• Explain your method to measure speeding using only simple techniques that could be
communicated to (and carried out by) the community.
• Explain how safe driving could be promoted to the community.
• Consider and evaluate your proposals from the point of view of One World.

RIC Roll: Drive Safe
Criterion A: One World Criterion B: Communication in Science

What is the issue in a local context and Your group must present the project
how can Science be applied to it? proposal to the Rokko Island council.

Devise a science-based speed-safety You must communicate the scientific
campaign. Evaluate its implications basis of your programme clearly, using
within at least two contexts (moral, textual and graphical media.
ethical, social, economical, political)

Calculating Speed Practice
1. Three cyclists are in a 20km road race. A has an average speed of
30kmh-1, B is 25kmh-1 and C 22kmh-1. The race begins at 12:00.
a. What time does rider A complete the course?

d
v t
b. Where are riders B and C when A has finished?

0 10km 20km
B A
C
12:00

Cyclist clipart from: http://www.freeclipartnow.com/d/36116-1/cycling-fast-icon.jpg

Calculating Speed Practice
2. The speed limit is 40kmh-1. A car drives out of the car park and
covers 10m in just 3s. Calculate:
a. The speed of the car in kmh-1.

d
v t
b. The car comes to a stretch of road which is 25m long. What is the
minimum amount of time the car should to take to be under the
speed limit?

Car clipart from: http://www.freeclipartnow.com/transportation/cars/green-sports-car.jpg.html

What do you feel when…
… playing on a swing? (You know you’re not too cool for that)

… taking off on an aeroplane?

… driving at a constant 85kmh-1 on the freeway?

… experiencing turbulence on an aeroplane?

… cruising at high altitude on an aeroplane?

… slowing your bike to stop for a cat?

Acceleration is the rate of change in velocity of an object
origin 30 60 90 120 150 180

Which cars are experiencing acceleration?
Find out here: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm

Sketch distance – time graphs for
each car (on the same axes)

Distance
What do the shapes of the lines
tell us about the cars’ motion?

Time

Acceleration is the rate of change in velocity of an object
Acceleration can be positive (‘speeding up’) or negative (‘slowing down’).
An object at rest has zero velocity and therefore zero acceleration.
An object at constant speed in one direction is not changing its velocity
and therefore has zero acceleration.
Velocity is a vector – the rate of change of displacement of an object.
Displacement and velocity are direction-dependent.
Therefore, a change in direction is also a change in acceleration.

Δv
a= Δt

Acceleration
Change in velocity
Δv
a= Δt =
acceleration
Initial velocity – final velocity (ms-1)
Time (s)

Change in time

ms -2
“Metres per second per second”

Acceleration
a = 3ms-2
Time (s) Velocity
(ms-1)

Velocity (ms-1)
0 0
1
2
3
0
4 0 1 2 3 4
formula Time (s)

Acceleration
a = 3ms-2 12

Time (s) Velocity
(ms-1)
9

Velocity (ms-1)
0 0
6
1 3
2 6 3
3 9
0
4 12 0 1 2 3 4
formula Time (s)

Acceleration
a = 3ms-2 12

Time (s) Velocity
(ms-1)
9

Velocity (ms-1)
0 0
6
1 3
2 6 3
3 9
0
4 12 0 1 2 3 4
Time (s)
formula v = 3t The velocity – time graph is linear as it is constant acceleration.
This means it is increasing its velocity by the same amount each
time. What would the distance – time graph look like?

Acceleration
a = 3ms-2 A car accelerates at a constant rate of 3ms-2.
12

Time (s) Velocity Calculate its instantaneous velocity at 7.5s:
(ms-1) -1
9 a. in ms

Velocity (ms-1)
0 0
6 b. in kmh-1
1 3
2 6 3
Calculate the time taken to reach its
3 9 maximum velocity of 216kmh-1.
0
4 12 0 1 2 3 4
formula v = 3t Time (s)

Acceleration
a = 3ms-2 12
Time (s) Velocity Displace-
(ms-1) ment (m) 30
9
0

Velocity (ms-1)

Displacement (m)
1 6 18

2
3 9
3
3
4 0
0 1 2 3 4
Time (s)
formula
Determine the velocity and displacement of the object each second.
Plot the results on the graph.
Compare the shapes of the two graphs.

Acceleration
a = 3ms-2 12
(ms-1) ment (m) 30
9
0 0

Velocity (ms-1)

Displacement (m)
1 3 6 18

2 6
3 9
3 9
3
4 12 0
0 1 2 3 4
Time (s)
formula v = 3t
The displacement – time graph is curved as it is constant
acceleration – the rate of change of displacement increases.
This means it is increasing its velocity by the same amount each time.

Acceleration
a = 3ms-2 12
(ms-1) ment (m) 30
9
0 0 0

Velocity (ms-1)

Displacement (m)
1 3 3 6 18

2 6 9
3 9
3 9 18
3
4 12 30 0
0 1 2 3 4
Time (s)
formula v = 3t
The displacement – time graph is curved as it is constant acceleration
– the rate of change of displacement increases.
This means it is increasing its velocity by the same amount each time.

Acceleration
a = -2ms-2
Time (s) Velocity
(ms-1)

Velocity (ms-1)
0 10
1
2
3
0
4 0 1 2 3 4
Time (s)
formula

Acceleration
a = -2ms-2
Time (s) Velocity
(ms-1)

Velocity (ms-1)
0 10
1 8
2 6
3 4
0
4 2 0 1 2 3 4
Time (s)
formula

Acceleration
a = 2kmh-1s-1
Time (s) Velocity
(kmh-1)

0 10
1
2
3
0
4 0 1 2 3 4
Time (s)
formula

Acceleration
a = 2kmh-1s-1 18
Time (s) Velocity
(kmh-1)

Velocity (kmh-1)
0 10
1
10
2
3
4 0
0 1 2 3 4
formula Time (s)

How is it possible for an object
moving at constant speed to
experience acceleration, but not an
object moving at constant velocity?

Rokko Liner Project
Form a hypothesis.
Describe the motion in some suitable format
as you currently know it.

Make approximate predictions on
1. time between each station (MP  IC) and (IC  IK)
2. wait time at IC
3. top speed between MP and IC
4. top speed between IC and IK
5. acceleration leaving a station
6. acceleration arriving at a station

For variables, treat Independent Variable as time
Dependent Variable as displacement or velocity

Rokko Liner Project
Write-ups.

Read through the instructions once more – carefully!

By the end of today’s lesson:
• Data processing is complete and graphs ready
• Analysis of data has begun

Draft stages:

B
A C
velocity
D G
time
E F

C
B
D
distance

A

E

time

Describing Motion

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Describing Motion