This presentation is for my class to work through as teachers are on a series of PD days. It is based on a very bad One Direction joke cracked in a class about vectors.

1. One Direction Do Physics
Introduction to Kinematics
MrT

2. Scalars vs Vectors
Non-directional quantities Quantities with direction
Distance Displacement
How far an object travels along a path Position of an object in reference to an
origin or previous position
Speed Velocity
Rate of change of the position of an Rate of change of the position of an object
object, e.g. 20m/s in a given direction, e.g. 20m/s East
“per unit time”
Δd
Average speed or velocity
v= Δt Change in distance
or displacement
Change in time
More scalars: More vectors:
Time Acceleration
Energy Force
Mass Electric field
Volume

3. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
displacement (m)
20
10
time (seconds)

4. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
displacement (m)
20
10
time (seconds)

5. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
movement back towards origin
displacement (m)
20 (negative displacement)
movement away from origin
(positive displacement)
Remember: Velocity is a vector (it has magnitude and direction).
10
time (seconds)

6. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
displacement (m)
20
10
time (seconds)

7. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
25m
constant motion, so we can
easily find Δd and Δt.
displacement (m)
20
Δd 15m 15m/s
10 v= Δt
= 1s =
(away)
velocity is a vector, so you
must include the direction!
1 second time (seconds)

8. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
displacement (m)
20
10
time (seconds)

9. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
No change in displacement over time
displacement (m)
20 RESTING
therefore:
v = 0m/s
10
time (seconds)

10. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
displacement (m)
20
10
time (seconds)

11. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
constant motion, so we can
easily find Δd and Δt.
displacement (m)
20
Note: this time they’re
moving closer to the sensor.
Velocity will be negative.
10
time (seconds)

12. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
25m
displacement (m)
20
Δd -5m -10m/s
10
v= Δt
= 0.5s = (or 10m/s towards)
we’d determined that
movement away was positive
time (seconds) 0.5s

13. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
displacement (m)
20
10
time (seconds)

14. 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
• State their velocity at 4s.
• Calculate their velocity at 6.5s
• Calculate their average velocity (over the whole journey)
Displacement-time graph for the One Direction tour bus.
20
17.5m
displacement (m)
10
Δd 7.5m
v= Δt
= 10s =0.75m/s (away)
time (seconds)

15. 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 +

16. 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 Positive velocity, decreasing velocity. +
origin, slows, turns and
speeds up on return to
origin.

17. 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

18. 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.

19. 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.

20. Velocity and Vectors One Direction got some new toys.
They couldn’t point them in the same direction.
Draw velocity vector diagrams for each of these karts.
10km/h 16km/h 8km/h 20km/h
Use the known vector as the scale.

21. Velocity and Vectors One Direction got some new toys.
They couldn’t point them in the same direction.
Draw velocity vector diagrams for each of these karts.
10km/h 16km/h 8km/h 20km/h
Use the known vector as the scale.

22. One of the boys was sent to bed.
Three of the others had a kart race:
origin 30 60 90 120 150 180
Which karts are experiencing acceleration?
Find out here: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm
Read through the Acceleration lesson at the Physics Classroom:
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

23. Describe the motion in these graphs.
A B C
v v v
t t t
D E F
v d d
t t t

24. If the tour bus keeps going at the same speed in One Direction:
• They have constant velocity
• They are not accelerating
Δd
v= Δt Change in distance
or displacement
Change in time
If the tour bus is at rest, they have:
• zero velocity
• and zero acceleration
Acceleration is a vector: it has magnitude and direction.

25. Acceleration is a vector: it has magnitude and direction.
We usually think of acceleration as
• ‘speeding up’ These are more appropriate descriptors of
• ‘slowing down’. changes in speed than in velocity.
has direction!
Instead, think of acceleration as:
• ‘positive’ acceleration is same direction as velocity
• ‘negative’ acceleration is opposite velocity
Stop here and work through the page on acceleration at:
http://www.physicsclassroom.com/Class/1DKin/U1L1e.cfm

26. Acceleration
Change in velocity
Δv
a= Δt =
acceleration
final velocity – initial velocity (m/s)
Time (s)
Change in time
m/s/s
“Metres per second per second”
On the next pages, complete the tables and sketch
the graphs before you skip onto the solutions.

27. Acceleration
a = 3m/s/s
Time (s) Velocity
(m/s)
Velocity (ms-1)
0 0
1
2
3
0
4 0 1 2 3 4
formula Time (s)

28. Acceleration
a = 3m/s/s 12
Time (s) Velocity
(m/s)
9
Velocity (m/s)
0 0
6
1 3
2 6 3
3 9
0
4 12 0 1 2 3 4
formula Time (s)

29. Acceleration
a = 3m/s/s 12
Time (s) Velocity
(m/s)
9
Velocity (m/s)
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?

30. Acceleration
a = 3m/s/s 12
A car accelerates at a constant rate of 3m/s/s.
Time (s) Velocity Calculate its instantaneous velocity at 7.5s:
9 a. in m/s
(m/s)
Velocity (ms-1)
0 0
6 b. in km/h
1 3
2 6 3
Calculate the time taken to reach its
3 9 maximum velocity of 216km/h.
0
4 12 0 1 2 3 4
formula v = 3t Time (s)

31. Acceleration
a = 3m/s/s 12
Time (s) Velocity Displace-
(m/s) ment (m) 30
9
0
Velocity (m/s)
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.

32. Acceleration
a = 3m/s/s 12
Time (s) Velocity Displace-
(m/s) ment (m) 30
9
0 0
Velocity (m/s)
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.

33. Acceleration
a = 3m/s/s 12
Time (s) Velocity Displace-
(m/s) ment (m) 30
9
0 0 0
Velocity (m/s)
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.

34. Acceleration
a = -2m/s/s
Time (s) Velocity
(ms-1)
Velocity (m/s)
0 10
1
2
3
0
4 0 1 2 3 4
Time (s)
formula

35. Acceleration
a = -2m/s/s
Time (s) Velocity
(ms-1)
Velocity (m/s)
0 10
1 8
2 6
3 4
0
4 2 0 1 2 3 4
Time (s)
formula

36. Acceleration In this example, acceleration is constant.
Determine the acceleration, plot the velocity
over time and deduce the formula.
a = ___m/s/s
Velocity (m/s)
Time (s) Velocity Explain: what does this tell us about
(ms-1) acceleration?
0 6
1 3.5
2
0
3 0 1 Time (s) 2 3 4
4
formula

37. Acceleration
a = 2km/h/s
Time (s) Velocity
(kmh-1)
Velocity (km/h)
0 10
1
2
3
0
4 0 1 2 3 4
Time (s)
formula

38. Acceleration
a = 2km/h/s 18
Time (s) Velocity
(kmh-1)
Velocity (km/h)
0 10
1
10
2
3
4 0
0 1 2 3 4
formula Time (s)

39. Describe the journey of the One Direction tour bus.
20
D E
velocity (m/s)
C
10 B F
A
1 2 3 4 5 6 7 8 9 10
time (s)
Just as velocity is the rate of change of
position of an object, acceleration is the
rate of change in velocity.
You can use the same methods to
calculate acceleration from a graph.

40. Negative acceleration is opposite to velocity.
The tour bus is headed for a cliff!
• What is the velocity of the bus after 3s?
• Does it stop in time?
v = 20m/s vector diagrams can be used (to scale) to
a = -2m/s/s represent velocity and acceleration.
100m

41. Negative acceleration is opposite to velocity.
The tour bus is headed for a cliff!
• What is the velocity of the bus after 3s?
• Does it stop in time?
v = 20m/s The bus starts at 20m/s and accelerates at -
a = -2m/s/s 2m/s/s.
• After 1s it is going at 18m/s
100m • After 2s is is going at 16m/s
• After 3s it is going at 14m/s.
What is the formula?

42. Negative acceleration is opposite to velocity.
The tour bus is headed for a cliff!
• What is the velocity of the bus after 3s?
• Does it stop in time?
v = 20m/s The bus starts at 20m/s and accelerates at -
a = -2m/s/s 2m/s/s.
• After 1s it is going at 18m/s
100m • After 2s is is going at 16m/s
• After 3s it is going at 14m/s.
What is the formula?
v = 20 – 2t

43. Negative acceleration is opposite to velocity.
The tour bus is headed for a cliff!
• What is the velocity of the bus after 3s?
• Does it stop in time?
v = 20 – 2t
t (s) v (m/s) d (cumulative, m)
v = 20m/s
a = -2m/s/s 0 20 0
100m 1 18 20
2 38
3
4
5
6
7
8

44. Negative acceleration is opposite to velocity.
The tour bus is headed for a cliff!
• What is the velocity of the bus after 3s?
• Does it stop in time?
v = 20 – 2t
t (s) v (m/s) d (cumulative, m)
v = 20m/s
a = -2m/s/s 0 20 0
100m 1 18 20
2 16 38
3 14 54
4 12 68
5 10 80
6 8 90
7 6 98
8 4 102!

45. Acceleration due to gravity is 9.8m/s/s (downwards).
Luckily the boys jump clear as the bus goes over the cliff.
What is the velocity of the bus after:
• 2s?
• 5s?
a = 9.8m/s/s
Find out: what is terminal velocity?

46. Acceleration is a vector: it has magnitude and direction.

47. Acceleration is a vector: it has magnitude and direction.
Did someone say New Directions?
Any change in direction is a change in
velocity and is therefore an acceleration.

48. Acceleration is a vector: it has magnitude and direction.
Did someone say New Directions?
Any change in direction is a change in
velocity and is therefore an acceleration.
How is it possible for an object
moving at constant speed to
experience acceleration, but not an
object moving at constant velocity?

49. 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

50. Challenge Question:
How far did the One Direction tour bus travel in 10 seconds?
20
velocity (m/s)
10
1 2 3 4 5 6 7 8 9 10
time (s)

51. Challenge Question:
When can an object experience acceleration
but have a velocity of zero?

52. Exit Ticket Take one minute to answer all three.
I got it!
•
I don’t get it!
•
One of your own
•

53. That’s what makes
Physics beautiful!
THE ONE DIRECTION TOUR BUS
Images adapted from http://www.fanpop.com/spots/one-direction/images/28558025/title & http://goo.gl/zJnql

54. TOUR BUS
NEW DIRECTIONS
Images adapted from http://newspaper.li/new-directions/& http://www.vectis.co.uk/

56. For more resources.
Please consider a donation to charity via Biology4Good.
Click here for more information about Biology4Good charity donations.
This is a Creative Commons presentation. It may be linked and embedded but not sold or re-hosted.