RECTILINEAR MOTION
Contents
Particular's Page No.
Theory 001 – 025
Exercise - 1 026 – 031
Part - I : Subjective Question
Part - II : Only one option correct type
Part - III : Match the column
Exercise - 2 032 – 034
Part - I : Only one option correct type
Part - II : Numerical value
Part - III : One or More than one option correct type
Part - IV : Comprehension
Exercise - 3 034 – 035
Part - I : JEE(Advanced) / IIT-JEE Problems (Previous Years)
Part - II : JEE(Main) / AIEEE Problems (Previous Years)
Answer Key 036
High Level Problems (HLP) 037 – 038
Subjective Question
Answer Key 039
JEE (ADVANCED) SYLLABUS
Kinematics in one Dimensions.
JEE (MAIN) SYLLABUS
Motion in a straight line : Position time graph, speed and velocity. Uniform and non-uniform motion,
average speed and instantaneous velocity Uniformly acceleration motion, velocity-time, position-time
graphs, relations for uniformly accelerated motion.
©Copyright reserved.
All rights reserved. Any photocopying, publishing or reproduction of full or any part of this study material is strictly prohibited. This material belongs to only the
enrolled student of RESONANCE. Any sale/resale of this material is punishable under law. Subject to Kota Jurisdiction only.
,Rectilinear Motion
RECTILINEAR MOTION
—————————————————————————————————
1. MECHANICS
Mechanics is the branch of physics which deals with the cause and effects of motion of a particle, rigid
objects and deformable bodies etc. Mechanics is classified under two streams namely Statics and
Dynamics. Dynamics is further divided into Kinematics and Kinetics.
2. MOTION AND REST
Motion is a combined property of the object and the observer. There is no meaning of rest or motion
without the observer. Nothing is in absolute rest or in absolute motion.
An object is said to be in motion with respect to a observer, if its position changes with respect to that
observer. It may happen by both ways either observer moves or object moves.
3. RECTILINEAR MOTION
Rectilinear motion is motion, along a straight line or in one dimension. It deals with the kinematics of a
particle in one dimension.
3.1 Position
The position of a particle refers to its location in the space at a certain moment of time. It is concerned
with the question “where is the particle at a particular moment of time?”
3.2 Displacement
The change in the position of a moving object is known as displacement. It is the vector joining the
initial position ( r1 ) of the particle to its final position ( r2 ) during an interval of time.
r2
Displacement can be negative positive or zero.
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Website : www.resonance.ac.in | E-mail :
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ADVRM - 1
, Rectilinear Motion
3.3 Distance
The length of the actual path travelled by a particle during a given time interval is called as distance.
The distance travelled is a scalar quantity which is quite different from displacement. In general, the
distance travelled between two points may not be equal to the magnitude of the displacement between
the same points.
Solved Example
Example 1. Ram takes path 1 (straight line) to go from P to Q and Shyam takes path 2 (semicircle).
2
P Q
1
100 m
(a) Find the distance travelled by Ram and Shyam?
(b) Find the displacement of Ram and Shyam?
Solution :
(a) Distance travelled by Ram = 100 m
Distance travelled by Shyam = (50 m) = 50 m
(b) Displacement of Ram = 100 m
Displacement of Shyam = 100 m
—————————————————————————————————
3.4 Average Velocity (in an interval) :
The average velocity of a moving particle over a certain time interval is defined as the displacement
divided by the lapsed time.
displacement
Average Velocity =
timeinterval
for straight line motion, along x-axis, we have
x x f x i
vav = v = <v> = =
t t f ti
–1
The dimension of velocity is [LT ] and its SI unit is m/s.
The average velocity is a vector in the direction of displacement. For motion in a straight line, directional
aspect of a vector can be taken care of by +ve and -ve sign of the quantity.
3.5 Instantaneous Velocity (at an instant) :
The velocity at a particular instant of time is known as instantaneous velocity. The term “velocity”
usually means instantaneous velocity.
x dx
Vinst. = lim =
t 0 t
dt
In other words, the instantaneous velocity at a given moment (say, t) is the limiting value of the average
velocity as we let t approach zero. The limit as t 0 is written in calculus notation as dx/dt and is
called the derivative of x with respect to t.
Note :
The magnitude of instantaneous velocity and instantaneous speed are equal.
The determination of instantaneous velocity by using the definition usually involves calculation
dx
of derivative. We can find v = by using the standard results from differential calculus.
dt
Instantaneous velocity is always tangential to the path.
Reg. & Corp. Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)– 324005
Website : www.resonance.ac.in | E-mail :
Toll Free : 1800 258 5555 | CIN : U80302RJ2007PLC024029
ADVRM - 2
Contents
Particular's Page No.
Theory 001 – 025
Exercise - 1 026 – 031
Part - I : Subjective Question
Part - II : Only one option correct type
Part - III : Match the column
Exercise - 2 032 – 034
Part - I : Only one option correct type
Part - II : Numerical value
Part - III : One or More than one option correct type
Part - IV : Comprehension
Exercise - 3 034 – 035
Part - I : JEE(Advanced) / IIT-JEE Problems (Previous Years)
Part - II : JEE(Main) / AIEEE Problems (Previous Years)
Answer Key 036
High Level Problems (HLP) 037 – 038
Subjective Question
Answer Key 039
JEE (ADVANCED) SYLLABUS
Kinematics in one Dimensions.
JEE (MAIN) SYLLABUS
Motion in a straight line : Position time graph, speed and velocity. Uniform and non-uniform motion,
average speed and instantaneous velocity Uniformly acceleration motion, velocity-time, position-time
graphs, relations for uniformly accelerated motion.
©Copyright reserved.
All rights reserved. Any photocopying, publishing or reproduction of full or any part of this study material is strictly prohibited. This material belongs to only the
enrolled student of RESONANCE. Any sale/resale of this material is punishable under law. Subject to Kota Jurisdiction only.
,Rectilinear Motion
RECTILINEAR MOTION
—————————————————————————————————
1. MECHANICS
Mechanics is the branch of physics which deals with the cause and effects of motion of a particle, rigid
objects and deformable bodies etc. Mechanics is classified under two streams namely Statics and
Dynamics. Dynamics is further divided into Kinematics and Kinetics.
2. MOTION AND REST
Motion is a combined property of the object and the observer. There is no meaning of rest or motion
without the observer. Nothing is in absolute rest or in absolute motion.
An object is said to be in motion with respect to a observer, if its position changes with respect to that
observer. It may happen by both ways either observer moves or object moves.
3. RECTILINEAR MOTION
Rectilinear motion is motion, along a straight line or in one dimension. It deals with the kinematics of a
particle in one dimension.
3.1 Position
The position of a particle refers to its location in the space at a certain moment of time. It is concerned
with the question “where is the particle at a particular moment of time?”
3.2 Displacement
The change in the position of a moving object is known as displacement. It is the vector joining the
initial position ( r1 ) of the particle to its final position ( r2 ) during an interval of time.
r2
Displacement can be negative positive or zero.
Reg. & Corp. Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)– 324005
Website : www.resonance.ac.in | E-mail :
Toll Free : 1800 258 5555 | CIN : U80302RJ2007PLC024029
ADVRM - 1
, Rectilinear Motion
3.3 Distance
The length of the actual path travelled by a particle during a given time interval is called as distance.
The distance travelled is a scalar quantity which is quite different from displacement. In general, the
distance travelled between two points may not be equal to the magnitude of the displacement between
the same points.
Solved Example
Example 1. Ram takes path 1 (straight line) to go from P to Q and Shyam takes path 2 (semicircle).
2
P Q
1
100 m
(a) Find the distance travelled by Ram and Shyam?
(b) Find the displacement of Ram and Shyam?
Solution :
(a) Distance travelled by Ram = 100 m
Distance travelled by Shyam = (50 m) = 50 m
(b) Displacement of Ram = 100 m
Displacement of Shyam = 100 m
—————————————————————————————————
3.4 Average Velocity (in an interval) :
The average velocity of a moving particle over a certain time interval is defined as the displacement
divided by the lapsed time.
displacement
Average Velocity =
timeinterval
for straight line motion, along x-axis, we have
x x f x i
vav = v = <v> = =
t t f ti
–1
The dimension of velocity is [LT ] and its SI unit is m/s.
The average velocity is a vector in the direction of displacement. For motion in a straight line, directional
aspect of a vector can be taken care of by +ve and -ve sign of the quantity.
3.5 Instantaneous Velocity (at an instant) :
The velocity at a particular instant of time is known as instantaneous velocity. The term “velocity”
usually means instantaneous velocity.
x dx
Vinst. = lim =
t 0 t
dt
In other words, the instantaneous velocity at a given moment (say, t) is the limiting value of the average
velocity as we let t approach zero. The limit as t 0 is written in calculus notation as dx/dt and is
called the derivative of x with respect to t.
Note :
The magnitude of instantaneous velocity and instantaneous speed are equal.
The determination of instantaneous velocity by using the definition usually involves calculation
dx
of derivative. We can find v = by using the standard results from differential calculus.
dt
Instantaneous velocity is always tangential to the path.
Reg. & Corp. Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)– 324005
Website : www.resonance.ac.in | E-mail :
Toll Free : 1800 258 5555 | CIN : U80302RJ2007PLC024029
ADVRM - 2
