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Summary Kinematics One Short Revision
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It's a complete revision notes of kinematics for Jee Mains & Advance and also for class 11th and class 12th board exams
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QUIZRR 1KINEMATICS
1
Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs,
and equations. The goal of any study of kinematics is to develop sophisticated mental models which
serve to describe (and ultimately, explain) the motion of real-world objects.
1 .1 SCA L A RS A N D V ECT ORS :
The motion of objects can be described by words - words such as distance, displacement, speed, velocity,
and acceleration. These mathematical quantities which are used to describe the motion of objects can
be divided into two categories. The quantity is either a vector or a scalar. These two categories can be
distinguished from one another by their distinct definitions:
Scalars are quantities which are fully described by a magnitude alone.
Vectors are quantities which are fully described by both a magnitude and a direction.
As you proceed through the lesson, give careful attention to the vector and scalar nature of each
quantity.
CH ECK Y OU R U N DERST A N DI N G
To test your understanding of this distinction, consider the quantities listed below. Categorize each
quantity as being either a vector or a scalar.
Quantity Category
a. 5m Scalar
b. 30 m/sec, East Vector. A direction is listed for it.
c. 20 degrees Celsius scalar
V e c t o r r e p r e s e n t a t i o n i n 2 -D:
The base vectors of a rectangular x-y coordinate system are given by the unit vectors i→ and →j along
the x and y directions, respectively.
j
y
i
F
F
y
x
Fx
Using the base vectors, one can represent any vector F as
F Fxi→ Fy →j
IITJEE KINEMATICS
, 2 QUIZRR
V e c t o r r e p r e s e n t a t i o n i n 3 -D:
In a rectangular coordinate system the components of the vector are the projections of the vector along
the x, y, and z directions. For example, in the figure the projections of vector A along the
x, y, and zdirections are given by Ax, Ay, and Az, respectively.
K
Z
A
Az j
y
i Ax
x Ay
A A xi→ A y →j Az k→
1 .2 A B ODY I N M OT I ON :
A body is said to be motion, when its changes its position with time, with respect to an observer.
Similarly, if the position doesnÊt change with time, with respect to an observer (reference), the body is
in rest.
Basic terms :
1. Particle : A particle is a point mass. However, in practice a body may be treated as a particle,
if its size is very small compared to the distance covered by it.
2. Position : The position of a particle refers to its location in the space at a certain moment of
time. In general the position is measured by a vector joining a fixed point (known as origin)
to the moving particle. This vector is known as position vector.
For a particle in straight line motion along X-axis, the position vector is always parallel to X-axis and
hence has only X-component as non-zero. Therefore the position of a moving particle can be measured
by the X-coordinate x (t) at a certain time instant t.
If a particle is moving in a curve (i.e. in a plane) the position vector can have many possible directions.
The position in such a case can be measured by two numbers : X-coordinate and Y-coordinate the
position vector.
y
A(x ,y)
r
o x
3. Distance is a scalar quantity which refers to „how much ground an object has covered‰ during
its motion. It is the actual length of the path travelled by a particle.
4. Displacement is a vector quantity which refers to „how far out of place an object is‰. It is the
vector joining the initial position of the particle to its final position during an interval of time.
The change in the position of a moving object is known as displacement
KINEMATICS IITJEE
, QUIZRR 3
(a) To test your understanding of this distinction, consider the m otion depicted in the diagram
below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters
North.
4m
2m 2m
4m
Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters.
During the course of her motion, she has „covered 12 meters of ground‰ (distance = 12 m). Yet, when
she is finished walking, she is not „out of place‰ i.e., there is no displacement for her motion (displacement
= 0 m). Displacement, being a vector quantity, must give attention to direction. The 4 meters east is
canceled by the 4 meters west; and the 2 meters south is canceled by the 2 meters north.
(b) If a particle goes from A to B along a curve in some time duration and if O is the origin then
B
OA = initial position vector = r1
A s
OB = final position vector = rf
rf
AB = displacement vector = OB OA
r
i
s rf ri r
O
5. Speed: Speed is a scalar quantity which refers to „how fast an object is moving. „Rate of
change of distance (x) covered by a particle, with time is called the speed of the particle. Its
unit is m/s.
Velocity is
6. Velocity: Velocity is a vector quantity which refers to „the rate at Speed with
which an object changes its position.‰ Rate of change of a direction.
displacement of the particle with time is called velocity of the
particle.
7. Average speed: The average speed of a particle in a time interval is defined as the distance
travelled by the particle by the time interval. If the particle travels a distance s in time t1 to
t2 the average speed is defined as:
s
speed av
t2 t1
8. Average velocity: The average velocity of a particle in a time interval t1 to t2 is defined as
its displacement divided by the time interval.
s x y
vav s displacement i→ →j
t2 t1 t t
IITJEE KINEMATICS
, 4 QUIZRR
Di f f e r e n c e b e t w e e n a v e r a g e s p e e d a n d a v e r a g e v e l o c i t y :
Consider a particle moving around a circle. A particle starts at point P in the circle and covers the entire
circumference of the circle and reaches back at point P (as given in the figure below):
p
Total distance travelled
In this case, Average speed =
Time taken
2r circumference of the circle
=
Time taken
On the contrary, magnitude of average velocity = 0, since displacement is 0.
9. Instantaneous speed: The instantaneous speed is the speed of the particle defined for a
particular instant. When we had described average speed, it meant speed of the particle
defined for a time interval.
Suppose a particle covered a distance s for a time interval t, then average speed in this case
s
is equal to
t
Now, if the interval t is made extremely small, approaching to zero, the speed that is defined
s ds
become for an instant. So, we can write the instantaneous speed as lim .
t 0 t dt
In general, when we talk of ÂspeedÊ, it refers to the instantaneous speed.
You might think of the instantaneous speed as the speed which the speedometer 40 50 60
30 70
reads at any given instant in time and the average speed as the average of all the 20 80
m/s
speedometer readings during the course of the trip. 10 90
0 100
0 0 0
meters
10. Instantaneous velocity: The velocity at a particular moment of time is known as instantaneous
velocity. The term ÂvelocityÊ usually refers to the instantaneous velocity.
11. Acceleration: Rate of change of velocity with time is called acceleration. Acceleration is a
vector quantity. Its unit is m/s2.
Di re c t io n o f t h e A c c e l e r a t i o n V e c t o r
Acceleration is a vector quantity so it will always have a direction associated with it. The direction of
the acceleration vector depends on two factors:
whether the object is speeding up or slowing down
whether the object is moving in the positive (+) or negative ( ) direction
The general RULE OF THUMB is :
If an object is slowing down, then its acceleration is in the opposite direction of its motion.
This RULE OF THUMB can be applied to determine whether the sign of the acceleration of an
object is positive or negative, right or left, up or down, etc.
KINEMATICS IITJEE
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