3 Pius Augustine_Kinematics

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Kinematics

Scalars: Physical quantities
which can be completely
specified by magnitude.
Eg: distance, speed , time etc.
Vectors : require both magnitude
and direction for complete
specification .
Eg: velocity , displacement ,
force etc.
2
Dr. Pius Augustine, S H College, Kochi

Kinematics and dynamics
Kinematics – study of
motion without
cause.
Dynamics - study of
cause of motion. 3

Statics – study of
bodies at rest
Dynamics – study of
bodies in motion/cause
of motion. 4

One, two and three dimensions
One dimension represents a
straight line
Two dimensions – plane
Three dimensions - space

Define a point object?
An object whose size is
negligible as
compared to the
distance moved by it.
6

Can earth be regarded as a point
object when it is describing its
yearly journey round the sun?
Yes, because the diameter of the
earth is very small as compared to
the radius of the orbital path (or
circumference) of the earth around
the sun.
7

8

9

11

12

13

Distance ?
Length of the path
traversed by a body.
Scalar quantity
SI unit – m
CGS unit – cm. 14

Displacement ? unit?
The Shortest distance
from the initial to the final
position of the body is
called the displacement .
SI unit - meter
cgs unit - cm 15

Note: Displacement is the distance
b/w initial and final positions.
If a body comes back to its initial
position, displacement will be
zero, but distance will be non zero
Displacement can be +ve, -ve or
zero, but distance is always +ve.
Magnitude of displacement can
never be greater than distance. 16

A boy leaves his home and goes on
a car, returning to his home after
travelling 20km in half an hour.
What is his average displacement?
The displacement is zero,
because the initial and final
positions are same.
17

Speed ?
The rate of change of
distance with time is
called the velocity.
Scalar qty
SI unit - m/s
CGS unit - cm/s 18

Uniform speed
If a body covers equal distance in
equal interval of time (however
small the interval may be)
Eg. Motion of a ball on a frictionless
surface.
19

Non Uniform or Variable speed
If a body covers unequal
distance in equal interval
of time.
Eg. … 20

Instantaneous Speed ?
For a body moving with
variable speed, speed at
any instant is called
instantaneous speed.
Eg. Speedometer of a car.
21

Which speed is
measured by the
speedometer of
your vehicle ?
Instantaneous speed

Average speed?
Of a body moving with variable
speed is that constant speed with
which body can cover same
distance in same interval of time
as it does with variable speed.
Is equal to the ratio of total distance
traveled by the body to the total
time of journey .
23

Velocity ?
The rate of change of
displacement with time is called
the velocity.
Vector qty
SI unit - m/s
CGS unit - cm/s
Speed in definite direction 24

Uniform motion ?
If a body makes equal
displacements in equal interval
of time (however small the
interval may be ) .
The velocity of motion will be a
constant in this case.
25

Can the speed of a body be
negative ?
No
It is the distance travelled in
unit time. Distance cannot
be negative.
26

Define acceleration?
Acceleration is the rate of
change of velocity with
time.
SI unit - m/s2
CGS unit - cm/s2
27

Can a body have zero velocity, yet
possess acceleration?
Yes
When a body is projected upwards,
at the highest point its velocity is
zero but the acceleration is g.
28

Can object have constant
speed but variable
velocity ?
Yes, in uniform
circular motion.
29

Acceleration ?
Rate of change of
velocity w.r.t. time is
called acceleration.
vector quantity
SI unit is m/s2
30

Define kinematics
The branch of physics, which
deals with the study of
mechanical motion of bodies
without considering the forces
that cause this motion, is
called kinematics.
31

Point object
An object is said to be a point
object, if its dimensions are
negligible as compared to
the distance travelled by it.
32

A boy leaves his home and goes
on a car, returning to his home
after travelling 20km in half an
hour. What is his displacement?
Zero ,
initial and final positions same
33

What does the area of acceleration
– time graph represent ?
Change in velocity
ie. at = v - u
34

What does the tangent at a point
to the position – time graph for an
object in non – uniform motion
along a straight line represent ?
Instantaneous speed or
velocity at the given
instant .
35

What do you understand by
positive and negative time?
The instant of time which is taken after
the origin of time (zero time) is called
positive time and the instant of time
which is taken before the origin of
time is called the negative time.
36

Can a body have a constant
velocity, but a varying speed?
No
Since velocity is speed plus
direction; therefore a body cannot
possess a constant velocity but a
varying speed.
37

When will be the relative velocity of
two moving objects be zero?
When two objects are moving
with equal/same speed in
the same direction.
38

Are rest and motion absolute or
relative terms?
Rest and motion are
relative terms
39

When will the distance and
displacement of a moving object be
the same in magnitude?
Body moves in straight
line in same direction
40

Can position – time graph be a
straight line parallel to time – axis?
No
Because body will have infinitely
high velocity to be at different
positions which is not possible.
41

What does the slope of position
– time graph indicate?
Velocity of the object.
42

When does position – time graph
have a negative slope ?
When the speed of the
body is decreasing.
43

Under what condition is the
average velocity equal to
instantaneous velocity ?
When body is moving with
uniform velocity ie one
dimension. 44

Can displacement be greater than
distance traveled by an object ?
No.
Displacement of an object can
be either equal to or less than
the distance travelled by the
object. 45

What is the numerical ratio of
velocity to speed of an
object?
Either less than or
equal to one
46

Are the magnitude of average
velocity and speed equal?
No they are often unequal
Average velocity and average
speed will be equal only in case of
a uniform motion of a body along a
straight line.
Av.vel = av. Speed = uniform velocity
47

What does slope of
velocity time graph
represent?
Acceleration
48

Acceleration due to gravity (g)
Acceleration acquired by a
freely falling body due to
gravitational pull of earth.
49

A ball is thrown straight up. What
is its velocity and acceleration at
the highest point?
Velocity = 0
Acceleration = 9.8 m/s2 downward
50

Two stones of different sizes are
dropped simultaneously from the
top of a building. Which stone would
reach earlier?
Both reach together
51

What is the nature of the
displacement time curve of a
body moving with constant
velocity?
Straight line passing
through origin
52

Is it possible that the average
velocity of a body is zero when
its average speed is not zero?
Yes
When the body returns to
the starting point.
53

Can position – time graph be a
straight line parallel to position –
axis?
No
Body will have different positions
at the same time which is
impossible
54

Does the value of acceleration due to
gravity remain the same at all places
of earth? Explain
No
Varies from place to place
Maximum at poles
Minimum at equator
55

Why is uniform linear motion not an
accelerated motion?
In uniform linear motion
neither the speed nor the
direction of motion
change. 56

Uniform circular motion is
accelerated motion. Comment .
In uniform circular motion
magnitude velocity is same but
direction of velocity changes
continuously. Hence it is
accelerated motion.
57

A body covers half its journey with a
speed of ‘a’ m/s and the other half
with a speed of ‘b’ m/s. Calculate
the average speed of the body
during the whole journey.
Hint: Average speed = Total
distance /total time.
Find t1 and t2 and take total
distance as 2x 58

Rectilinear motion
Motion in a straight line

Kinematics
Study of motion without
going into the cause of
motion.
60

Point object
Size of the object is negligible
compared to the distance
moved by it.
61

Origin
Any fixed point in space from
where the three co ordinate
axes (x.y and z) originate.
62

Position
It is the position of an object in
space w.r.to the co ordinate axes
at a given instant of time.
In case of motion in a straight line,
there is only one axis
conventionally called the x-axis.
If the distance from origin is x at
time t, this position is represented
as x(t). 63

Path length or Distance
The distance moved by
the object in the given
time.
64

Displacement
Shortest distance of the final
position of the object from its initial
position in the the direction from
the initial position to the final
position
65

Distance vs displacement
i.Actual
distance .
ii. No direction
iii. Only positive
value
iv. Scalar
quantity
i. Shortest
distance
ii. Direction from
initial to final
iii. poisitive, 0, or
–ve.
iv.Vector qty .
66

Speed
Time rate of covering the distance
by an object.
Scalar m/s MoLT-1.
Only zero or positive.
Only quantitative knowledge, how
fast the object is moving .
Nothing about direction. 67

Velocity
Time rate of change of
displacement of an object.
Vector has direction .
m/s MoLT-1.
+ve , 0 or -ve 68

Uniform velocity
If undergoes equal
displacements in equal
intervals of time, however small
these intervals may be.
69

Variable or non uniform vel.
Either speed of direction
of motion or both change
with time.
70

Average vel
It is that uniform velocity with
which an object will cover the
same displacement in same
interval of time as if it does with
variable velocity during that
time interval. 71

Instantaneous velocity
The velocity of an object a a
particular instant of time or
at a particular point of its
path is inst.vel.
72

Straight line parallel to time axis
73

Activity
• Try to think about the nature of the
following graphs/different sections of
the graphs.
• Make questions
• Plot new graphs based on your
understanding and put questions
across. 74

76

77

78

79

80

87

88

89

97

Relative velocity
Velocity of an object relative
to another object which may
be stationary or moving.

Draw position time
graph for two objects
moving with equal
velocities?
99

Draw position time
graph for two objects
moving with unequal
velocities?
100

Acceleration
Rate of change of
velocity w.r.to time.
101

Average acceleration
Total change in
velocity in a given
time interval to the
time interval
102

Variable
acceleration?
103

The area under an acceleration-time graph gives the velocity of an object
104

Equations of motion
i. V = u+at
ii.S = ut +1/2at2.
iii.V2 = u2 + 2aS
iv.Sn = u + a (n-1/2)
106

Sn = u+ a (n-1/2)
This equation is applicable only if
direction of velocity and
acceleration are same
Above formula does not hold good
otherwise, as the modulus of
displacement will not be equal to
distance.
Sn is displacement in the nth
second.
107

speed but varying velocity?
Yes
Uniform circular motion
108

velocity but varying speed?
No
109

Is it possible to have
displacement zero, not
distance?
Yes
110

What is the numerical
ratio of velocity to
speed of an object?
Either less than or equal to one
.
111

In which case average
speed equals velocity?
Uniform velocity
112

Under what condition the distance
and displacement of a moving
object will have the same
magnitude?
• Moving in straight line
always in same direction.
113

What does the
speedometer of a car
measure?
Instantaneous speed .
114

If the acceleration of a particle is
constant in magnitude but not in
direction, what type of path will the
particle follow?
•Non linear path
115

What do you get from
area under v-t graph
displacement
116

What will be the nature of
x-t graph for a uniform
motion
Straight line inclined with
time axis. 117

Can x-t graph be a
straight line parallel
to position axis?
No.
Object has different
positions at same time 118

What does the tangent at a point to the
position time graph for an object in non
uniform motion along a straight line
represent?
• Instantaneous speed or velocity
119

The displacement time graph for
two particles A and B are straight
lines inclined at angles of 30oand
45owith the time axis. What is
ratio of the velocities va: vb
120

How can the distance
traveled be
calculated from v-t
graph
121

What does the area under
acceleration – time graph of a body
moving with variable acceleration.
Change of speed of the body
during that time interval. 122

Can a body have
zero velocity and still
be accelerating ?
Yes
Highest point of a body
projected upwards. 123

Can the direction of
velocity of a body change,
when acceleration is
constant ?
Yes,
At highest point of a body
projected upwards , velocity
direction changes. 124

Is it possible to have a
constant rate of change of
velocity when velocity
changes both in magnitude
and direction ?
•Yes,
•In projectile. 125

Displacement x = 1+2t+3t2.
find the value of instantaneous
acceleration?
Hint: Differentiate twice, a = 6 units.
126

A train moving on horizontal rails
with a uniform acceleration a. A
passenger sitting in a bogey drops
a stone inside a the bogey . What
will be the acceleration of stone i)
w.r.to bogey ii) w.r.to rails?
i. g
ii. (a2+g2)1/2
127

A ball is thrown vertically
upwards.
Draw its velocity – time graph
128

A man standing on the edge of a cliff throws
a stone straight up with initial sped u and
then throws another stone straight down
with same initial speed and from the same
position. Find the ratio of the speeds, the
stones would have attained when they hit
ground at the base of the cliff?
130

Can an object be accelerated
without speeding up or
slowing down?
Yes
Uniform circular motion
131

What will be the ratio of the
distance moved by a freely
falling body from rest in 4th and
5th second of its journey ?
7/9 132

Give examples
i. +ve velocity with
deceleration
ii. -ve velocity with –ve accn
iii.Zero velocity with +ve accn
iv.Increasing velocity with
–ve accn
133

Draw position time graphs for
two objects initially occupying
different positions but having
zero relative velocity.
134

Graphically show that distance
covered by a particle in nth
second is Sn = u +1/2a (2n-1)
Difference in area of two
trapezium
135

A particle in one dimensional motion
with positive value of acceleration must
be speeding up. Is it true ? Explain .
Depends on the choice of +ve direction of
position axis.
Eg. Freely falling body - +ve direction is
vertical line downward.
Body projected vertically upwards, positive
direction of position axis is regarded as to
be opposite to the direction of motion,
body slows down instead of speeding up.136

Is the rate of change of acceleration
with time important to mechanics ?
Comment .
Can be defined, but not important.
Because basic laws of motion involve only
acceleration .
Galelio and Newton discovered that to
understand and explain motion , it is enough
to define velocity and acceleration.
137

Which of the two – velocity or
acceleration decides the direction
of motion of a body. Explain with
examples?
Velocity
(when a body is retarded, body will move in the
direction velocity, but acceleration is opposite.
2. When body is moving in circular path,
acceleration is towards the centre, but velocity is
along the tangent, which is the expected
direction of motion of the body)
138

If the distance covered by a moving
object varies directly as the time, what
conclusion could you draw about the
motion and the force ?
x = kt.
Differentiating , v = k constant
Body moving with uniform
velocity
139

If the displacement of a body is
proportional to square of time, state
whether the body is moving with
uniform velocity or uniform acceleration
x = kt2., k constant
Differentiating , v = 2kt,
ie. v depends on time – variable vel.
Differentiating again, a = 2k , constant.
Ie. accn, is independent of time –
uniform accn 140

2 particles are moving with constant speed v
such that they are always a constant distance
d apart and their velocities are always equal
and opposite. After what time do they return
to their initial position ?
They must be at the two ends of the diameter of a
circular path . The diameter of this circular path = d.
Each particle will return to its initial position after
describing a circular path = 2πr = πd
141

A particle moves on three quarters of
the circumference of a circle of radius
r. what are the values of the
displacement and distance traveled by
the body?
142

A train 100m in length is moving
with a velocity of 60km/h. In
what time it does it cross a
1km long bridge?
Hint: s = 1100m
t = s/v
143

If a man’s swimming speed with and
against the water current in a river be
15km/h and 5km/h , then find out the
man’s speed in still water and the
speed of the river.
Hint : vm+vw = 15
vm-vw = 5
144

A car travels along a straight line with speed
40km/h from A to B and returns back from
B to A with speed 60km/h. what are the
average speed and average velocity of the
car ?
Ans : 50km/h , zero
145

A cyclist starting from the centre O of a circular
track having radius 1km, reaches the edge A of
the track , thereafter cycles along the
circumference and stops at point B .(less than
one complete circular motion , angle BOA =
60o ). If the total time taken is 10minutes ,
determine i) average velocity and ii) average
speed.
Ans: i) 6km/h, ii) 12.3 km/h 146

A body moves along a straight line such
that its displacement s at any time t is
given by s = t3-6t2+3t+4, where s is in
meters and t in seconds. Determine the
velocity , when the acceleration is zero .
Hint: differentiate twice , put a = 0, t= 2s,
put value of t = 2s in equation for velocity . V = -9m/s
147

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3 Pius Augustine_Kinematics

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