1. The document discusses various concepts related to one-dimensional motion including position, distance, displacement, speed, velocity, and acceleration. 2. It defines key terms like displacement as the change in position of an object, velocity as a vector quantity that includes both speed and direction, and acceleration as the rate of change of velocity with respect to time. 3. Examples and equations are provided to calculate quantities like average speed, average velocity, and instantaneous velocity from distance-time graphs or data tables.

1. POSITION, DISTANCE, &
DISPLACEMENT
AVERAGE SPEED AND VELOCITY
INSTANTANEOUS VELOCITY
By Chaiporn Pattanajak
CHAPTER 2
Line Motion (one Dimension Motion)

2. It is a change in the position of
an object with respect to time.
Section I :
POSITION, DISTANCE & DISPLACEMENT
Straight

3. Let’s look the picture

4. Introduce
• Motion
Motion is a change of position or displacement of an object
within a certain time interval

5. Let’s look the picture

6. Old position
Let’s look the picture
Old positionNew position
New position
A
B
Can you tell me about rockets A and rockets B!

7. Old position
Let’s look the picture
Old position
New position
New position
A
B
We can say, rocket A moving and B No !
Moving object is identified by its change
of position from a certain point of
reference

8. A change of position or displacement of
an object from a certain point of
reference is called MOTIONMOTION

9. Frame of reference (กรอบ
อ้างอิง)Definition : A frame of reference is an extended
Object whose parts are at rest relative to each
other.
Frame of reference
Initial Position Final Position

10. •Displacement is a
vector and so must
have a distance
value andand aa
direction.direction. VectorVector
quantity.quantity.
•Distance just has a
value. Scalar
quantity
Start Point
Finish Point
A
B
(Initial Position)
(Final Position)

11. • Set up a coordinate system
–Right is usually positive, left is usually
negative
– Distance = total length of travel
– Displacement = change in position = final
position – initial position or ∆x = xf - xi
• Displacement can be positive, negative, or

12. • What is your distance traveled if you
start at your friend’s house travel to
the grocery store then back to your
house?
• What is your displacement for the
same route?
• What are some routes that you could
take to have a negative displacement?
• How about a displacement of zero?

13. In this section you are able to :
1. Making a graph of displacement vs
time
2. Finding the equation of speed
3. Identifying the application of
constant straight motion in daily life
Section II
:
• Average Speed and
Velocity

14. Speed is scalar quantity.
(Blue curve)
time
cedis
v
tan
=
Unit :
m/s
Velocity is vector quantity. (Green line)
time
ntdisplaceme
v =

Unit :t
x
tt
xx
v
if
if
∆
∆
=
−
−
=


t
x
tt
xx
v
if
if
∆
∆
=
−
−
=
ix
fx

15. • Point of referent is location which is considered fixed (at rest) and
used to compare the initial and final position.
• To understand how fast the object moves we have to know time
needed to travel the distance of displacement.

16. Base on component that
contents of quantities,
quantities can be derived in
two kind :
1. Vector (velocity)
2. Scalar (speed)

17. Velocity
For example
1. If some one walking 5 km/hour toward east :
a. his speed is 5 km/hour
b. his velocity is 5 km/hour to east.

18. Average Speed and Velocity
• Average speed = distance/elapsed time

19. Average Speed and Velocity Con’t.
• Average velocity = displacement/elapsed
time
• Sign tells the direction of the object motion
– + sign means xf > xi
– – sign means xf < xi

20. Instantaneous Velocity
 Average velocity isn’t very descriptive about the
exact rate of motion of an object at a specific
time
 Ideally you would calculate the average velocity
for every minute or second
 Instantaneous velocity, v =
– When the velocity is constant, average velocity over
any time interval = instantaneous velocity at any
time
– When the velocity changes, the instantaneous
velocity at a given time is equal to the slope of the
tangent line at that point on a displacement vs. time
graph

21. Graphical Interpretation of Average
Velocity
 Slope of a line connecting two
points on an displacement vs.
time plot is equal to the average
velocity during that time interval

22. distancedistance
(m)(m)
time (s)time (s)
d1d1 t1t1
d2d2 t2t2
GraphGraph
d (m)
d2
d1
0 t1 t2 t (s)
VelocityVelocity

23. Handout
d (m)
d2
d1
0 t1 t2 t (s)
GrahpGrahp
Const
t
d
t
d
==
2
2
1
1
VelocityVelocity
This Constant is Called
Velocity

24. When drawing graphs, follow these steps:
• Decide what data goes on the x-axis and what
data goes on the y-axis.
• Title your graph and label the axes, remember to
include units.
• Have even scales on your axes. (i.e. 1, 2, 3, 4 …
not 1, 2, 5, 8 …)
• Plot your points on the graph. Make sure to start
at 0.
• Connect points with a ruler for distance-time and
speed-time graphs.
Draw a graph using this data.Copy

25. You have to be able to describe what isYou have to be able to describe what is
happening in a distance-time graph…happening in a distance-time graph…

26. Handout

27. 1. The vehicle covered 100km in the first
two hours.
2. The vehicle was stationary between 2
hours and 5 hours.
3. Between 5 hours and 8 hours the vehicle
covered a further 180 km.
4. Between 8 hours and 11 hours, the
vehicle was stationary.

28. Velocity
Velocity is the change of position within a time interval
If distance (d), time interval (t) and velocity (v), we can write formula of
velocity
t
d
v =

29. The relationship among d, t, and v
t
d
v =
v
d
t =
tvd .=
d
v t

30. Calculating the velocity
Average speed is the total traveled distance divided by the time needed to
travel that distance.
∑
∑=
t
d
v
v = average speed
Σd = total distance
Σt = time total

31. •We can use the
slopeslope of a
distance – time
graphs to find the
speed of an
object.
•To do this the
graph line must
be straight.straight.
t
x
Slope
∆
∆
=
Copy
Slope = velocity

32. Handout

33. Calculate the slopeslope for each Car
•The average speed of Car A =
•The average speed of Car B =
•The average speed of Car C =

34. Time (h) Speedometer
Car A (kmh-1
)
0 50
0.5 50
1.0 50
1.5 50
2.0 50
2.5 50
3.0 50
3.5 50
4.0 50
Copy

35. •Plot a speed – time graph using this
data for Car A.
Speed (kmh-1
)
Time (s)

36. Speedometer Car B
(kmh-1
)
80
80
80
0
0
0
80
80
80
• Just add
another
column to the
table you
have already
drawn.
Copy

37. •Just add the Car B data to the graph
you already have.
•You will need to make the Car B line
different to the Car A line.
•Use two colours or crosses and dots.

38. Speedometer
Car C (kmh-1
)
0
10
20
30
40
50
60
• Just add
another
column to the
table you
have already
drawn.

39. *Just add the Car C data to the graph
you already have.
*You will need to make the Car C line
different to the Car A and Car B lines.

40. Time (s) Speed Skier
1 (ms-1
)
Speed Skier
2 (ms-1
)
0 0 0
1 5 10
2 10 20
3 15 30
4 20 40
5 25 50
Copy

41. •Plot a speed – time graph using this data.
•Plot the two skiers on the same axes.
•Draw a straight line of best fit for both
skiers (use a ruler).
Speed (ms-1
)
time (s)

42. •Calculate the slope of the two
skiers.
•How quickly was skier 1
accelerating?
•How quickly was skier 2
accelerating?

44. Aim of the experiment:
To measure how the height of a ramp
affects the speed of a marble covering 1m along
flat ground.
Equipment:
•2x 1m rulers (one with a dip in it)
•Clamp stand
•Stopwatch
•Marble

45. Method:
Conduct this experiment in pairs (or groups of 3 max).
1.Measure a clamp stand so that it is 10cm above the ground.
2.Place a ruler on the clamp stand. This will work as the ramp.
3.At the end of the ramp (lying flat on the ground), place the
second ruler.
4.Let the marble travel down the ramp.
5.Start timing the marble when it hits the flat surface, and time
how long it takes to travel the 1m.
6.Repeat the experiment with the clamp at 10cm, so that you have
3 times.
7.Repeat the experiment with the clamp at 20cm, 30cm and
40cm. Make sure you have 3 times for each height.

46. Processing your data:
1.Average your times for each ramp
height.
2.Draw a graph using the averages.
3.From your data, calculate the
average speed of the marble for each
ramp height.
4.Calculate the acceleration of the
marble for each ramp height.

47. This is calculated
from speed-time
graphs.
Once you have split up your graph, use the formula
to find the area of each shape:
Square or rectangle = x-axis X y-axis [base X height]
Triangle = ½ X(x-axis X y-axis) [½ X base X height]
Copy
To do this, graphs need to
be split into squares or
rectangles or triangles.

48. You may have more than one shape on a
graph.
When this happens, work out the area of
each shape separately and then add the
areas together.
Handouts x2 – Finding the Area under
Graphs and Distance from a speed-
time graph

49. Km
Hours

52. Straight Motion
Straight motion is motion that have

53. Identify pleace!

54. Identify pleace!