1. Describing Motion
Introduction to Kinematics
2012-13
Stephen Taylor & Paul Wagenaar
Canadian Academy, Kobe
Canadian Academy inspires students to inquire,
reflect and choose to compassionately
impact the world throughout their lives.
2. 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/
3. 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?”
Significant concept:
Change can be communicated using descriptions,
graphical representations and quantities.
Whee! By Todd Klassy, via the Physics Classroom Gallery
http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
4. How can we describe change?
Whee! By Todd Klassy, via the Physics Classroom Gallery
http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
• Distinguish between scalars and vectors.
• Distinguish between distance and displacement.
• Describe displacement of an object using components (coordinates), magnitude and direction
and directed line segment vector diagrams.
• Describe motion of an object in a given direction based on positive and negative displacement.
• Calculate distance and displacement from a map.
• Plot distance and displacement graphs from raw data or a strobe diagram
• Distinguish between instantaneous and average speed/velocity.
• Calculate average speed and velocity from a displacement-time graph or set of recorded data.
• Analyze a displacement-time graph to show various types of motion (constant, resting,
direction etc).
• Analyze a velocity-time graph to describe changes in motion.
• Draw and analyze vector diagrams to show velocity (magnitude and direction)
• Convert velocity in km/h to m/s and vice-versa.
• Calculate distance (displacement), speed (velocity) or time from a word equation giving other
key information.
• Define acceleration.
• Calculate acceleration from a set of data.
• Deduce a formula to determine instantaneous velocity from a given acceleration.
• Explain why objects moving at constant speed can experience acceleration, but not those
moving at constant velocity.
5. Where are we going?
http://www.slideshare.net/gurustip/qr-orienteering-rokko-island
Complete the QR Code orienteering course
to learn about describing motion using:
• scalars and vectors
• components
• magnitude and direction
• directed line segments
6. North
South
EastWest
“North of West”
“East of North”
“ South of East”
“ West of South”
“West of North”
“South of West”
“ East of South”
“ North of East”
Where are we going?
7. North
South
EastWest
“North of West”
“East of North”
“ South of East”
“ West of South”
“West of North”
“South of West”
“ East of South”
“ North of East”
origin
A B
C
D
E
F
G
m.socrative.com/student/
Room: N304
8. Three ways of describing displacement
N
E
Components (coordinates or directional descriptors)
- e.g. 3mE, 2mN of origin
Magnitude and Direction
- described, e.g. 2.1m 35oN of West
Vectors (directed line segments)
- direction and magnitude are important
North
West
3m
2m
9. Scalars vs Vectors
Non-directional quantities
Distance
How far an object travels along a path
Speed
Rate of change of the position of an object,
e.g. 20m/s
Quantities with direction
Displacement
Position of an object in reference to an
origin or previous position
Velocity
Rate of change of the position of an object
in a given direction, e.g. 20m/s East
“per unit time”
v= Δd
Δt
Average speed or velocity
Change in distance
or displacement
Change in time
More scalars:
Time
Energy
Mass
Volume
More vectors:
Acceleration
Force
Electric field
10. Where are we going?
Formative assessed task for Criterion E: Processing Data.
As a group, present your completed course map,
calculations and summary of what you learned on a
poster. Comment on the reliability of the data.
Individually design a new, 4-point course using all
methods of describing displacement. Location 4 may not
be back at the origin. Calculate total distance and
displacement for the course.
11. Where are we going?
Individually design a new,
4-point course.
Draw vector diagrams on the
map.
Two moves must be
described using components.
Two moves must be
described using magnitude
and direction.
Calculate total distance
along vector diagrams.
Calculate total displacement
from the origin.
This includes direction.
Show all working.
1
2
3
4
12. http://www.youtube.com/watch?v=gWnfqSxp-Dc
Unstoppable A runaway train with no brakes and a load of really
dangerous chemicals is heading right for your town.
How long have you got?
What questions do you need to ask?
Train cartoon from: http://www.mytrucks.co.uk/how_to_draw_a_steam_train.htm http://en.wikipedia.org/wiki/CSX_8888_incident
13. http://www.youtube.com/watch?v=gWnfqSxp-Dc
Unstoppable A runaway train with no brakes and a load of really
dangerous chemicals is heading right for your town.
How long have you got?
Train cartoon from: http://www.mytrucks.co.uk/how_to_draw_a_steam_train.htm
A B
113.4km
v t
d
210m in 10s
http://en.wikipedia.org/wiki/CSX_8888_incident
x
14. How do I convert between m/s and km/h?
km
h
=1 m
s = m
s
15. How do I convert between m/s and km/h?
km
h
=1 m
s = m
s
1000
60 x 60
1000
3600.
To convert from m/s to km/h, multiply by 3.6.
To convert from km/s to m/s, divide by 3.6.
1 m/s = 3.6km/h
km/hm/s
x 3.6
÷ 3.6
16. Calculating Speed Practice
Cyclist clipart from: http://www.freeclipartnow.com/d/36116-1/cycling-fast-icon.jpg
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?
b. Where are riders B and C when A has finished?
12:00
0 20km10km
AB
C
v t
d
17. 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.
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
v t
d
18. This is how far we’ve got.
19. Splish Splash MrT and Mr Condon go swimming in the 25m
RICL pool. Mr C is way faster than MrT.
Free swimmer clipart from: http://www.clker.com/clipart-swimming1.html
How long does it take MrC to lap MrT?
How would you work it out?
25m in 18s25m in 20s
MrCMrT
20. Are drivers speeding outside school?
http://www.youtube.com/watch?v=Qm8yyl9ROEM
1 mile = 1.61km
The speed limit is 40km/h.
Convert this to m/s.
What are some of the One
World issues related to
speeding drivers?
In what ways could science
be used to catch or prevent
speeding drivers?
21. Are drivers speeding outside school?
Aim: Test a quick method using cones and timers to determine whether a car is
speeding outside the school or not. The speed limit is 40km/h.
• Choose one of the methods on the following slides.
• Record as many cars as you can in 15 minutes.
• Show working of your calculations.
• Consider uncertainties and errors in your results.
v= Δd
Δt
20m
Car Distance (m)
±0.1m
Time (s) ± ____
s
Speed m/s ± ___ Speed km/h ±
___
1 20
2 20
3 20
4 20
5 20
22. Measure the time taken for cars to cover 20m. Record all cars
passing school over a 15 minute period.
Calculate each recording as m/s.
Determine how many cars are breaking the speed limit of
40km/h. Show your working in the conversion from m/s to
km/h.
Calculate the minimum time a car must take to pass between
the cones whilst remaining within the speed limit.
Evaluate the method, noting limitations and
possible improvements.
Are drivers speeding outside school?
v= Δd
Δt
20m
23. Are drivers speeding outside school?
v= Δd
Δt
Free app: http://itunes.apple.com/us/app/simple-radar-
gun/id442734303?mt=8
20m
Measure the speed of all the cars that pass by the school in a
15-minute period. Determine how many cars are breaking
the speed limit of 40km/h.
Outline the conversion the app uses to get from metres and
seconds to km/h.
Calculate each recording as m/s.
Calculate the minimum time a car must take to pass between
the cones whilst remaining within the speed limit.
Evaluate the method, noting limitations and
possible improvements.
24. The local speed limit is 40kmh-1.
If we adopt the method of putting markers at set
distances along each road, can you rearrange the
equation so that local people can determine whether or
not a car is speeding – just by counting?
t.v = d
t = d
v
v= Δd
Δt
Sampled distance (you decide)
This example: 50m
50m
40kmh-1
50m
40 x 1000
3600( )
50m
11.1ms-1
4.5s= = ==
Are drivers speeding outside school?
25. Are drivers speeding outside school?
Evaluate the method:
• Are data reliable? (enough repeats, acceptable uncertainty/error)
• Are data valid? (did we measure what we set out to measure?)
• What are the limitations of the method, how might they have impacted the
results and how could they be improved?
26. Representing motion graphically
Sketch two curves for Michael Johnson:
• Distance/time
• Displacement/time http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m18s
Distinguish between distance and
displacement.
0
4515 30
400
200
100
300
time (seconds)
d(metres)
27. 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
away from the sensor
towards the sensor
28. 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
resting
resting
Fast constant motion
Slow constant motion
away from the sensor
towards the sensor
29. Walk This Way Using LoggerPro to generate distance/time graphs.
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.
30. 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
(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 East
(metres per second to the East)
31. 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.
32. Calculating Speed
v= Δd
Δt
At what speed did the object move away from the sensor?
v= Δd
Δt
33. Calculating Speed
v= Δd
Δt
At what speed did the object move away from the sensor?
Δd
Δt v=
34. Calculating Speed
v= Δd
Δt
At what speed did the object move away from the sensor?
2.5m – 1m = 1.5m
Δd
Δt 3s – 1s = 2s
v= 1.5m
2s
35. Calculating Speed
v= Δd
Δt
At what speed did the object move away from the sensor?
2.5m – 1m = 1.5m
Δd
Δt 3s – 1s = 2s
v= 1.5m
2s
= 0.75m/s
36. Calculating Speed
v= Δd
Δt
At what speed did the object move away from the sensor?
2.5m – 1m = 1.5m
Δd
Δt 3s – 1s = 2s
v= 1.5m
2s
= 0.75m/s
(2d.p.)
37. Calculating Speed
v= Δd
Δt
At what speed did the object move toward the sensor?
v=
Δt
Δd
38. Calculating Speed
v= Δd
Δt
At what speed did the object move toward the sensor?
Δd
Δt
v=
Δt
Δd
39. Calculating Speed
v= Δd
Δt
At what speed did the object move toward the sensor?
2.5m – 1.75m = 0.75m
Δd
Δt 7.5s – 6s = 1.5s
v= 0.75m
1.5s
= 0.5m/s
Remember: speed is a
scalar, not a vector, so
direction is not important
(don’t use negatives)
40. Instantaneous Speed
v= Δd
Δt
Is the speed of an object at any given moment in time.
X
X
X
X
X
no line
41. Instantaneous Speed
v= Δd
Δt
Is the speed of an object at any given moment in time.
v = 0.5m/s
v = 0.75m/s
v = 0.00m/s
v = 0.00m/s
v = 0.00m/s
X
X
X
X
X
42. Average Speed
v= Δd
Δt
Is the mean speed of an object over the whole journey.
v= 1.5m + 0.75m
10s
= 0.225m/s
ΔdΔd +
Δt = 10 seconds
“mean”
Every movement adds to
the total distance traveled
43. Calculating Velocity
v= Δd
Δt
At what velocity did the object move away from the sensor?
v= Δd
Δt
44. Calculating Velocity
v= Δd
Δt
At what velocity did the object move away from the sensor?
Δd
Δt v=
45. Calculating Velocity
v= Δd
Δt
At what velocity did the object move away from the sensor?
2.5m – 1m = 1.5m
Δd
Δt 3s – 1s = 2s
v= 1.5m
2s
46. Calculating Velocity
v= Δd
Δt
At what velocity did the object move away from the sensor?
2.5m – 1m = 1.5m
Δd
Δt 3s – 1s = 2s
v= 1.5m
2s
= 0.75m/s(away from sensor)
When the person moves away
from the sensor, distance and
displacement are the same.
47. Calculating Velocity
v= Δd
Δt
At what velocity did the object move away from the sensor?
1.75m – 2.5m= -0.75m
Δd
Δt
v= 0.75m
1.5s
= -0.5ms-1
(toward sensor)
When the person moves toward
the sensor, displacement is lost.
48. 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.
NNorth is positive. East is positive. South is positive.
49. 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.
NNorth is positive. East is positive. South is positive.
+ve
+ve
-ve
-ve
zero
50. 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.
NNorth is positive. East is positive. South is positive.
+ve
+ve
-ve
-ve
zero
-ve
-ve
+ve
+ve
+ve
51. 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.
NNorth is positive. East is positive. South is positive.
+ve
+ve
-ve
-ve
zero
-ve
-ve
+ve
+ve
+ve
zero
-ve
-ve
+ve
+ve
52. Instantaneous Velocity
v= Δd
Δt
Is the velocity of an object at any given moment in time.
X
X
X
X
53. Instantaneous Velocity
v= Δd
Δt
Is the velocity of an object at any given moment in time.
v = 0.75m/s
v = 0.00m/s
v = 0.00m/s
X
X
X
X
54. Instantaneous Velocity
v= Δd
Δt
Is the velocity of an object at any given moment in time.
v = -0.5m/s
v = 0.75m/s
v = 0.00m/s
v = 0.00m/s
X
X
X
X
Velocity is a vector.
It is direction-specific.
This point moving closer to the
origin can be negative.
55. Average Velocity
v= Δd
Δt
Is the mean velocity of an object over the whole journey.
v=
“mean”
56. Average Velocity
v= Δd
Δt
Is the mean velocity of an object over the whole journey.
v= 1.75m – 1.00m
10s
= 0.075m/s
Δd
Δt = 10 seconds
“mean”
(away from sensor)
57. Comparing Speed and Velocity
v= Δd
Δt
v= 0.075m/s (away from sensor)
v= 0.225m/sMean speed
Mean velocity
Mean speed is non-directional. ∆d = all distances
Mean velocity is directional. ∆d = total displacement
58. Calculating Speed & Velocity
v= Δd
Δt
Calculate the following in your write-ups.
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
59. Walk This Way Using LoggerPro to generate distance/time graphs.
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.
60. Explain this!
Distance from sensor (m)
Velocity (ms-1)
61. Explain this!
Distance from sensor (m)
Velocity (ms-1)
Speeding up Slowing
Changing direction
Speeding up
(falling) Caught
Changing direction
Resting
Resting
Let go
Going upwards Falling
Speeding up
Slowing Speeding up
Caught
62. 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 clarifications to make
sure you achieve a good grade
63. Calculating values on a curve
Distance from sensor (m)
Time (s)
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.
X
What about here?
64. Calculating values on a curve
Distance from sensor (m)
Time (s)
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.
X
What about here?
A triangle is not representative of the curve!
65. Calculating values on a curve
Distance from sensor (m)
Time (s)
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.
X
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.
66. Calculating values on a curve
Distance from sensor (m)
Time (s)
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.
X
Now the triangle fits the point.
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.
67. Calculating values on a curve
Distance from sensor (m)
Time (s)
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.
X
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.
Now the triangle fits the point.
v= Δd
Δt
(0.6m – 0.25m)
(0.4s)
= = 0.875m/s
68. This is a displacement-time graph for the One-Direction tour bus.
• Did they really go in one direction? How do you know?
• Calculate their velocity at 2s
• Calculate their average velocity (over the whole journey)
69. Speed and Velocity
A ball is thrown up in the air and caught. Determine:
a. The instantaneous velocity of the ball at points A and B
b. The average velocity of the ball.
v= Δd
Δt
Time (s)
10.50
1
2
A
B
70. Velocity and Vectors
Velocity is a vector – it has direction.
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.
v= Δd
Δt
Describe the motion in these velocity vector diagrams:
+
origin
origin
origin
+
origin +
Positive velocity, increasing velocity.
71. Velocity and Vectors v= Δd
Δt
Describe the motion in these velocity vector diagrams:
+
origin
origin
origin
+
origin +
Object moves quickly
away from origin, slows,
turns and speeds up on
return to origin.
Positive velocity, increasing velocity.
Negative velocity, increasing velocity.
Positive velocity, decreasing velocity.
Velocity is a vector – it has direction.
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.
Positivevelocity,decreasingvelocity.
Negativevelocity,increasingvelocity.
72. 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.
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)
55cm
1.6m
7.5 m
The birds are angry that the pigs destroyed their
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.
73. 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.
74. 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.
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.
75. Velocity and Vectors
Draw velocity vector diagrams for each of these karts.
10km/h 16km/h 8km/h 20km/h
Use the known vector as the scale.
76. Velocity and Vectors
Draw velocity vector diagrams for each of these karts.
Use the known vector as the scale.
10km/h 16km/h 8km/h 20km/h
77. Velocity and Vectors
A rugby ball is displaced according to the vector below, for 0.6 seconds.
Determine the velocity of the ball.
2m
30o
78. Velocity and Vectors
A rugby ball is displaced according to the vector below, for 0.6 seconds.
Determine the velocity of the ball.
2m
30o
v=
Δd
Δt =
10
0.6 = 16.7m/s
(30o up and forwards)
79. 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 85km/h on the freeway?
… experiencing turbulence on an aeroplane?
… cruising at high altitude on an aeroplane?
… slowing your bike to stop for a cat?
80. Acceleration is the rate of change in velocity of an object
Which cars are experiencing acceleration?
Find out here: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm
origin 30 60 90 120 150 180
Sketch distance – time graphs for
each car (on the same axes)
What do the shapes of the lines
tell us about the cars’ motion? Distance
Time
81. 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.
a=Δv
Δt
82. Acceleration
a=Δv
Δtacceleration
Change in velocity
Change in time
= Initial velocity – final velocity (m/s)
Time (s)
m/s/s
“Metres per second per second”
83. Acceleration
a = 3m/s/s
Time (s) Velocity
(m/s)
0 0
1
2
3
4
formula
0
0 1 2 3 4
Velocity(ms-1)
Time (s)
84. Acceleration
a = 3m/s/s
Time (s) Velocity
(m/s)
0 0
1 3
2 6
3 9
4 12
formula
12
9
3
0
6
0 1 2 3 4
Velocity(m/s)
Time (s)
85. Acceleration
a = 3m/s/s
Time (s) Velocity
(m/s)
0 0
1 3
2 6
3 9
4 12
formula v = 3t
12
9
3
0
6
0 1 2 3 4
Time (s)
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?
Velocity(m/s)
86. Acceleration
a = 3m/s/s
Time (s) Velocity
(m/s)
0 0
1 3
2 6
3 9
4 12
formula v = 3t
12
9
3
0
6
0 1 2 3 4
Velocity(ms-1)
Time (s)
A car accelerates at a constant rate of 3m/s/s.
Calculate its instantaneous velocity at 7.5s:
a. in m/s
b. in km/h
Calculate the time taken to reach its
maximum velocity of 216km/h.
87. Acceleration
a = 3m/s
Time (s) Velocity
(m/s)
Displace-
ment (m)
0
1
2
3
4
formula
12
9
3
0
6
0 1 2 3 4
Velocity(m/s)
Time (s)
Determine the velocity and displacement of the object each second.
Plot the results on the graph.
Compare the shapes of the two graphs.
3
9
18
30
Displacement(m)
88. Acceleration
a = 3m/s
Time (s) Velocity
(m/s)
Displace-
ment (m)
0 0
1 3
2 6
3 9
4 12
formula v = 3t
12
9
3
0
6
0 1 2 3 4
Velocity(m/s)
Time (s)
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.
3
9
18
30
Displacement(m)
89. Acceleration
a = 3m/s/s
Time (s) Velocity
(m/s)
Displace-
ment (m)
0 0 0
1 3 3
2 6 9
3 9 18
4 12 30
formula v = 3t
12
9
3
0
6
0 1 2 3 4
Velocity(m/s)
Time (s)
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.
3
9
18
30
Displacement(m)
90. Acceleration
0
0 1 2 3 4
Velocity(ms-1)
Time (s)
a = -2ms-2
Time (s) Velocity
(ms-1)
0 10
1
2
3
4
formula
91. Acceleration
0
0 1 2 3 4
Velocity(ms-1)
Time (s)
a = -2ms-2
Time (s) Velocity
(ms-1)
0 10
1 8
2 6
3 4
4 2
formula
92. Acceleration
0
0 1 2 3 4
Time (s)
a = 2kmh-1s-1
Time (s) Velocity
(kmh-1)
0 10
1
2
3
4
formula
93. Acceleration
0
0 1 2 3 4
Time (s)
a = 2kmh-1s-1
Time (s) Velocity
(kmh-1)
0 10
1
2
3
4
formula
Velocity(kmh-1)
10
18
94. How is it possible for an object
moving at constant speed to
experience acceleration, but not an
object moving at constant velocity?
95. How is it possible for an object moving at constant speed to
experience acceleration, but not an object moving at
constant velocity?
Image: Moon from northern hemisphere: http://en.wikipedia.org/wiki/Moon
96. Who’s faster?
Bolt vs Gump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196
http://www.youtube.com/watch?v=3nbjhpcZ9_g
Usain Bolt’s 100m world record:
100m0m
Gump
Bolt
Strobe diagram: each dot is the position of the runner after one second.
97. Graphing Motion
Bolt vs Gump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196
100m0m
Gump
Bolt
Sketch a distance/ time graph for Gump and Bolt.
Strobe diagram: each dot is the position of the runner after one second.
98. Graphing Motion
Bolt vs Gump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196
100m0m
Gump
Bolt
Plot a distance/ time graph for Gump and Bolt.
What other analysis can be carried out with these data?
Discuss and do it!
Strobe diagram: each dot is the position of the runner after one second.
99. Gump vs. Bolt
Bolt vs Gump, from
http://www.ew.com/ew/gallery
/0,,20220853_20499114,00.htm
l#20499196
Blog post: Describing Motion Review
Use the Gump vs Bolt data to write a blog post.
It will act as a review of the content of the unit (check the assessment statements
on your review sheet), as well as an informative article for others.
You can write it as:
• A local reporter for the Greenbow, Alabama paper
• A sports reporter writing about Bolt and the Olympics
• A straight-up scientific explainer for HS students
Look at the criteria and the assessment statements. As a small group, make
and share a list of task-specific clarifications. Check, draft, write, cite.
It will be assessed for Criterion B: Communication in Science:
100. Infographic from: http://www.telegraph.co.uk/sport/olympics/olympic_infographics_and_data/9453618/London-2012-
Olympics-battle-of-the-sprint-kings-Usain-Bolt-and-Yohan-Blake.html
Bolt vs Blake: What do the data tell us?
101. Unit Test: Describing Motion
Criterion C: Knowledge & Understanding in Science
102. Unit Test: Describing Motion
Criterion C: Knowledge & Understanding in Science
Reflection on the back of the test:
1. What have you learned during this ‘Motion’ unit
that you didn’t know before?
1. What have you learned about how you learn?
1. Do you think your performance in the test is a
good reflection of your learning? Why?
1. Do you think the test was fair and allowed you to
demonstrate what you had learned? How would
you improve it?
1. How will you build on this for next time?
If you’re done:
• Rokko Liner Plans!
103. Rokko Liner Project
104. Spare Slides
105. time
velocity
A
B
C
D
E F
G
distance
time
A
B
C
D
E
106. What are the coordinates of these objects?
origin
2mE, 1mN
Coordinates can be used to describe an objects position or displacement.
107. 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
______________________
108. 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
Big Squirrel
• 4mS to the
Enthusiastic Runner
• 2mS, 4mE to the
Tiny Cyclist
109. Pick a mystery object.
Describe the displacement to three other objects.
Can another group deduce the objects?
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.
110. Which objects are:
• 2.1m away from the origin at 14oN of East?
• 5m away from the origin at 30oN of East?
111. Which objects are:
• 2.1m away from the origin at 14oN of East?
• 5m away from the origin at 30oN of East?
112. Magnitude and Direction tell us the displacement in terms of
the most direct path.
E
N
origin
113. Magnitude and Direction can also be represented by directed
line segments (vector diagrams).
E
N
1m
The direction (angle relative to the
orientation) and magnitude (length of
the vector) are important.
114. Which objects lie closest to these vectors?
(directed line segments – hint, start at origin, length is important)
N
E
N
E
N
E
A
B
C
115. Which objects lie closest to these vectors?
(directed line segments – hint, start at origin, length is important)
N
E
N
E
N
E
A
B
C
116. Describing displacement
N
Components (coordinates or
directional descriptors)
- e.g. 3mE, 2mN of origin
Magnitude and Direction
- described, e.g. 2.1m 14oN of
origin
Vectors (directed line segments)
- direction and magnitude are
important
117. Describing displacement
N
Components (coordinates or
directional descriptors)
- e.g. 3mE, 2mN of origin
Magnitude and Direction
- described, e.g. 2.1m 14oN of
origin
Vectors (directed line segments)
- direction and magnitude are
important
118. 1km
N
$
Ke$ha’s Day Out on Rokko Island
Wake up feeling like P
Diddy
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.
119. 1km
N
$
Ke$ha’s Day Out on Rokko Island
Wake up feeling like P
Diddy
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.
Pedicure
Clothes
Club
120. 1km
N
$
Ke$ha’s Day Out on Rokko Island
Wake up feeling like P
Diddy
1. Calculate:
a. Total distance b. Total displacement c. Average speed d. Average velocity
e. Average speed on the walk home.
2. Describe the displacement
of the pedicurist from her house using:
a. directed line segment
b. direction and magnitude
Pedicure
Clothes
Club
121. Sketch a velocity-time graph for this journey.
0.5s
0.2m
Calculate velocity
before it hits the fabric.
122. Thrown up at 12m/s
Accelerates down at 10m/s/s
Hits water at 4s.
What is the velocity as it hits the water?
What is the height of the bridge?
123. Images adapted from http://www.fanpop.com/spots/one-direction/images/28558025/title & http://goo.gl/zJnql
THE ONE DIRECTION TOUR BUS