Topic 2: Representing
Motion
LO 2.1-2.4
Learning Objectives:
Which of the following
objects is moving?
What is motion?
• Motion is a change in position with respect to
a fixed point.
• To describe the motion of an object we need at least
two factors:
1- position (place) of the object.
2- time.
Particle model
A model where the
moving object is
represented by a point.
How far is Abu Dhabi?
How far is Abu Dhabi
• From Dubai?
126 km
• From RAK?
166 km?
• From Falaj Al Mualla?
216 km?
• The answer depends on the starting point!
Reference
Frame/
Coordinate
System
The coordinate system with the
origin as the reference point is
called frame of reference.
1-dimensional
coordinate system
2-Dimensional
coordinate system
Position
• Position of an object is how far from the origin is
the object with direction.
• Position is a vector quantity (has a magnitude and
direction)
• It’s direction is expressed as +/• Its symbol is “x”
• The SI unit of position is meter. Other units are
cm, km, etc..
+-
Position: ( / ) Convention
+ position is to the RIGHT
- position is to the LEFT
Xcat=+40 cm
Xdog=-20 cm
origin
-50 cm
-10 cm
-30 cm
-40 cm
-20 cm
0 cm
50 cm
30 cm
10 cm
20 cm
40 cm
+-
Position: ( / ) Convention
+ position is UP
- position is DOWN
50 cm
0 cm
Xcat=+10 cm
Xdog=-30 cm
-50 cm
origin
Lesson Summary
• Motion is a change in position with respect to a reference
frame.
• The coordinate system with the origin as the reference point
is called frame of reference
• Position of an object is how far from the origin is the object
with direction.
Scalars and Vectors
• In physics, quantities could be classified into two groups:
1- Scalar quantities.
2- Vector quantities.
• Scalar quantities are quantities that could be described by
magnitude (value and unit) only.
Examples: time, distance and speed
• Vector quantities are quantities that could be described by
magnitude (value and unit) and direction.
Examples: position, displacement, velocity and acceleration
Distance
• When an object changes its position with respect to origin
(moves), its motion is described by:
1- Distance
2- Displacement
• Distance is the length of the entire path travelled by an object.
• Distance is a scalar quantity, it is described only by magnitude.
• The SI unit of distance is meter (m).
• The distance travelled by an object depends on the path of the
travel.
Distance
Example 1:
An object travels from point A to point B. How much distance was
travelled by the object
A
B
m
Answer: Distance = 3 m
Example 2:
B
Answer: Distance = 5 m
A
m
Distance
Example 3:
An object travels from point A to point B then to point C as shown in the below
diagram. How much distance was travelled by the object
A
C
B
m
Answer: Distance = 5 + 3 = 8 m
Example 4:
C
Answer: Distance = 2 + 7 = 9 m
A
B
m
Distance
Example 5:
An object travels from point A to point B and comes back to point
A as shown in the below diagram. How much distance was
travelled by the object
A
Answer: Distance = 3 + 3 = 6 m
B
m
Define Displacement
• Displacement is the change in an object’s position
with respect to the origin. It can be positive or
negative.
Initial position
xi=0 cm
Displacement:
Dx = x f - xi
Dx = 9cm- 0cm= +9cm
Final position
xf=9 cm
Distance and displacement
• Displacement is a vector quantity, it is described by magnitude
and direction.
• SI unit: meter (m).
• Symbol: (∆x).
• Mathematically, displacement is the shortest length between
initial (starting) position and final (finishing) position with
direction
xi: the initial position
displacement = ∆x = xf - xi
xf: the final position
• The displacement of an object does not depends on
the path of the travel, it only depends on initial and final
positions.
Displacement
Example 6:
An object travels from point A to point B as shown in the below
diagram. What is the object’s displacement? Represent it with an
arrow.
A
Answer: xi = +1 m
∆x = xf - xi
B
m
, xf = +4 m
∆x = (+4) – (+1)
∆x = +3 m Notice that the displacement is positive
because the object travelled to the right
between the initial and final positions
Displacement
Example 7:
An object travels from point A to point B as shown in the below
diagram. What is the object’s displacement? Represent it using
an arrow.
B
Answer: xi = +1 m
∆x = xf - xi
A
m
, xf = -4 m
∆x = (-4) – (+1)
∆x = -5 m Notice that the displacement is negative
because the object travelled to the left
between the initial and final positions
Displacement
Example 8:
An object travels from point A to point B then to point C as shown in the below
diagram. What is the object’s displacement? Represent it using an arrow.
A
B
C
m
, xf = +4 m
Answer: xi = -4 m
∆x = xf - xi
∆x = (+4) – (-4)
∆x = +8 m
Notice that the displacement is positive
because the object travelled to the right
between the initial and final positions
Displacement
Example 9:
An object travels from point A to point B then to point C as shown in the below
diagram. What is the object’s displacement? Represent it using an arrow.
C
A
B
m
Answer: xi = +2 m , xf = -3 m
∆x = xf - xi
∆x = (-3) – (+2)
∆x = -5 m
Notice that the displacement is negative
because the object travelled to the left
between the initial and final positions
Displacement
Example 10:
An object travels from point A to point B and comes back to A as
shown in the below diagram. What is the object’s displacement?
Represent it using an arrow.
A
Answer: xi = +1 m
, xf = +1 m
∆x = xf - xi
∆x = (+1) – (+1)
∆x = 0
B
m
Compare and Contrast Distance and
Displacement
Distance
• Total distance travelled
• Scalar quantity and has
magnitude only
• Can only be +
Displacement
• Distance between starting
and final position
• Vector quantity has
magnitude and direction
• Can be +/-
They are both length
Both have SI unit: meter (m)