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UNIT TWO
Mechanics
and kinematics
Describing
motion
In
science,
Motion is defined as
 The change in position for a
particular time interval. You can
then start describing motion
with the question, “
How
far did the object travel?”
HOW FAR?
DISTANCE AND DISPLACEMENT
How far did the object travel?
There are actually two ways
to answer this question.
First is by getting the total
length of the path travelled
by the object.
Example: Ali ran 10m to the east, then
5m to the south, and another 10m to
the west. So it has travelled a total of 25
meters. (DRAW)
other way is by measuring the
distance between the initial
position and final position of the
object.
 The
 Ali
has travelled 5 meters to the south.
In
science, the first
measurement gives
the distance travelled
by the object while the
second measurement
gives its displacement.
Adobe
file: Here are more
illustrations showing the
difference between distance
travelled (represented by
broken lines) by an object and
its displacement (represented
by continuous lines).
 Can
you give one difference between
distance and displacement base on
the given examples?
P.O. C
Definition
Type of
quantity
Distance
Displacement
It is the actual
path that the
body covered
Scalar
It is the distance covered in a
certain direction
It is the shortest distance
between final and initial points
Vector
x1  x f  xi
 80 m  10 m
  70 m
x2  x f  xi
 20 m  80 m
  60 m
1-CALCULATE THE DISTANCE AND DISPLACEMENT
WHEN AN OBJECT MOVES FROM (A) TO (B).
2-CALCULATE THE DISTANCE AND DISPLACEMENT
WHEN AN OBJECT MOVES FROM (A) TO (A) AGAIN .
1-CALCULATE THE DISTANCE AND DISPLACEMENT
WHEN AN OBJECT MOVES FROM (A) TO (C).
2-CALCULATE THE DISTANCE AND DISPLACEMENT
WHEN AN OBJECT MOVES FROM (A) TO (A) AGAIN.
In which case can displacement be equal
to zero?
Is it possible to get zero displacement?
Speed
velocity
and
acceleration
Speed is the term used to describe
the distance traveled in a unit of
time
The distance can be in a straight
line or around a corner
1-
Speed
2-Instantaneous Speed :
the speed at any given instant in time=actual speed
speedometer
Example1
The physics teacher
walks 4 meters East, 2 meters South,
4 meters West, and finally 2 meters North. The entire motion
lasted for 24 seconds.
Determine the average speed.
Answer
The physics teacher walked a
distance of 12 meters in 24
seconds; thus, her average speed
was 0.50 m/s.
Velocity
Velocity is the term used to
describe the displacement traveled
in a unit of time
It describes how fast and in what
direction a body is moving
Now the formula :
V = displacement/time
For motion in straight line you
can use + or – to indicate the
direction
V=+ 10 m/s
V= -10 m/s
P.O. C
Speed
DEFINATION
It is the distance
traveled in a unit
of time
Type of
quantity
Scalar
𝒔
𝒗=
𝒕
Velocity
It is the displacement
traveled in a unit of
time
Vector
𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲 =
Displacement
Time
Acceleration
Acceleration is the rate of
change of velocity
►Acceleration has direction and magnitude.
►Thus, acceleration is a vector quantity.
http://www.youtube.com/watch?v=_BM89yVZoBg&mode=related&search=
Now the formula of accelerstion is :
∆𝒗
𝒂=
∆𝒕
𝒗−𝒖
𝒂=
𝒕𝒇 − 𝒕𝒊
𝒂 : Acceleration (m/s2 )
(𝒗( : 𝐟𝐢𝐧𝐚𝐥 𝐯𝐞𝐥𝐨𝐜𝐢𝐭𝐲 (m/s).
𝒖: initial velocity (m/s )
𝒕𝒇 : time of the end of motion( Sec )
: 𝒕𝒊 : time of the beginning of motion
∆v = change in velocity
( subtract, final – initial)
a = v-u
Motion graphs
Higher the speed more the gradient
Low speed means less
slope or gradient
High speed means more
slope or gradient
2. Speed or (velocity)
Vs time graphs
1. On a speed or (velocity) -time graph the gradient of the line is the acceleration
2. On a speed or (velocity ) - time graph the area under the the line is equal to
the distance or displacement traveled
Example1
In the graph below
describe the motion of the object?
•In region A the object is moving with constant acceleration.
•In region B the object is moving with constant velocity.
•In region C the object is again moving with
• constant acceleration, but when compared with region A:
1. the acceleration is slower because the slope is less steep
2. the acceleration is negative because the slope is downwards.
•The total distance travelled by the object can be
calculated by measuring the area under the graph.
This area can be divided into two triangles and one rectangle.
The area of triangle A = ½ base x height
= 0·5 x 10 x 20 = 100.
The area of triangle C= ½ x (70 - 30) x 20 = 400.
The area of rectangle B = (30 - 10) x 20 = 400.
The distance travelled is the total area = A + B + C
= 100 + 400 + 400 = 900 m.
Equation Of Motion
38
What are equation of motion?
• Whenever object moves and you want to
describe its motion…
• There are four equations of motion to find
The relationships between displacement, time,
velocity, and constant acceleration
• They apply if the motion is in a straight line
And acceleration is uniform
39
Five
Quantities
Or
Variables
40
Equation of motion
Does not include s
𝒗 = 𝒖 + 𝒂∆𝒕
1
∆𝒔 = 𝒖∆𝒕 + 𝒂 ∆𝒕
2
1
∆𝒔 = (𝒖 + 𝒗)∆𝒕
2
𝒗2 = 𝒖2 + 2𝒂∆𝒔
41
2
Does not include v
Does not include a
Does not include t
Derive the first equation of motion
𝑣−𝑢
𝑎=
∆𝑡
𝑣 − 𝑢 = 𝑎∆𝑡
𝒗 = 𝒖 + 𝒂∆𝒕
42
Example 1
-2
• A car accelerate form rest at 3ms
Along a straight road. How far does the
car travelled after 4 s??
S= 24 m
43
Example 2
• A car is travelling 20 m/s along a
straight road, The driver puts the
brakes on for 5 s. If this causes a
-2
deceleration of 3ms What is the car’s
final velocity?
-1
44
45
46
47
A racing car reaches a speed of 42 m/s. It then begins a uniform
negative acceleration, using its parachute and braking system, and
comes to rest 5.0 s later. Find the distance that the car travels during
braking.
.‫ بمعرفة سرعتها االبتدائية وزمن التوقف‬، ‫حساب المسافة الالزمة لتوقف سيارة‬
48
What is free fall
• Free falling is a motion under force of
.
gravity as the only force
acting on the
moving object.
• The acceleration on an object in free
fall is called the acceleration due to
gravity, or free-fall acceleration
• Practically, free falling can only
• take place in vacuum
Air Resistance
• In air…
– A stone falls faster than a
feather
• Air resistance affects
stone less
• In a vacuum
– A stone and a feather will
fall at the same speed.
• When air resistance
is negligible, mass
has no effect on the
downward motion
on an object.
. Free Fall
The acceleration of
gravity (g) for objects
in free fall at the
earth's surface is 9.8
m/s2.
Galileo found that all
things fall at the same
rate.
. Free Fall
The rate of falling
increases by 9.8 m/s
every second.
Height = ½ gt2
For example:
½ (9.8 )12 = 4.9 m
½(9.8)22 = 19.6 m
½ (9.8)32 = 44.1 m
½ (9.8)42 = 78.4 m
. Free Fall
Acceleration due to gravity is constant during
upward and downward motion.
Free-fall acceleration on Earth’s surface is
(9.8 𝑚/𝑠 2 ≈ 10 𝑚/𝑠 2 ) at all points
in the object’s motion.
When the body fall down the velocity increases
by rate = 9.8 m/s for each second
g = +9.8𝑚/𝑠 2
When the body thrown up the velocity decreases
by rate = 9.8 m/s for each second
g = -9.8𝑚/𝑠 2
. Equation of Motion for Free Fall
𝒗 = 𝒖 + 𝒈∆𝒕
𝟏
∆𝒅 = 𝒖∆𝒕 + 𝒈 ∆𝒕
𝟐
𝒗𝟐 = 𝒖𝟐 + 𝟐𝒈∆𝒅
𝟐
Free Fall - example
• 1) A coin is dropped in a vacuum tube, Find
the coin's velocity after.30 seconds.
• Vf = ?
•
•
•
•
•
•
•
t = .30 seconds
a = g = - 9.8 m/s2 (falling)
Vi = 0 m/s
vf = vi +at
Vf = vi +gt
Vf = 0 -10 m/s2 x .30 s
Vf = -3 m/s
Free Fall - example
2) If a rock is dropped from a building, and it
takes 18 seconds to reach the ground, how
tall is the building?
Sample Problem
– 1. A worker drops a wrench from the top of a
tower 80.0 m tall. What is the velocity when
the wrench strikes the ground?
– 2. How far above the floor would you need to
drop a pencil to have it land in 1 s?
– H.B solving problem numbers 1 and 2 page 27
Force
• There are forces all around us.
• We make use of forces to do a lot
of things in our everyday life.
• Force is a push or a pull acting
upon an object.
• Whenever we push or pull an
object, we exert a force.
• We cannot see a force, but we can
see and feel its effects.
• The following diagrams shows activities
that involve ………….forces.
• These diagrams shows activities that
involve Pushing forces
• The following diagrams show activities
that involve ………….. forces.
• The following diagrams show activities
that involve pulling forces.
Force
Touch Force
acts on an object
only
by touching it.
Normal force
Air Resistance
Force
Non Touch Force
acts at a distance
(long-range force).
Gravitational Force
Magnetic force
The effects of forces
• The effects of a force include
(a) force changes the shape of an object
(b) force changes the position of an
object
(c) force changes the speed of a
moving object
(d) force changes the direction of a
moving object
Force can change the shape of an object
• Pressing, bending and stretching can change
the shape of an object.
(a) Bending
(b) Stretching
(c) Pressing
Force changes the speed of a moving object such as:
i. Move it
ii. Stop it
iii.Increase or decrease its speed
force changes the position of an object
Hit a ball
move
move
Force changes the direction of a moving object.
• A force can change the direction of an
object's movement.
The unit of force
• We measure force in units called Newton (N).
• (1N resultant force acting on 1kg produces
an acceleration of 1m/s2).
• We can measure a force using a spring
balance or Newton meter.
Equal forced
• Two forces are equal
when the two forces
(magnitude) and
direction are the same.
Balanced forces
• When the forces acting on an object are
balanced, they cancel each other out.
The net force (RESULTANT) is zero.
• Effect :
the object at is at rest [ velocity = 0]
Question 1
Forces of 12 N and 5 N both act at the same point, but their
directions can be varied.
a) What is their greatest possible resultant?
b) What is their least possible resultant?
c) If the two forces are at right angles, find the resultant.
Question 2
Which one of the following effect of force
on an object is not true ?
A.Change its shape
B.Change its position or direction
C.Change its colour
D.Change its speed