Kinematic Class 11 Notes Physics

 Page 1


Physics Class XI
20
2.1 Motion in One Dimension : Position
Position of any point is completely expressed by two factors : Its distance  
 from the observer and its direction with respect to observer.
That is why position is characterised by a vector known as position vector.
Let point P is in a xy plane and its coordinates are (x, y). Then position  
 v ector of point will be  and if the point P is in a space and 
its coordinates are (x, y, z) then position vector can be expressed as 
2.2 Rest and Motion
If a body does not change its position as time passes with respect to frame 
of reference, it is said to be at rest.
And if a body changes its position as time passes with respect to frame 
of reference, it is said to be in motion.
Frame of Reference : It is a system to which a seet of coordinates are 
attached and with reference to which observer describes any event.
Rest and motion are relative terms. It depends upon the frame of references.
2.3 Types of Motion
      One dimensional    Two dimensional   Three dimensional
Motion of a body in a straight Motion of body in a plane Motion of body in a space
line is called one dimensional is called two dimensional is called three dimensional
motion. motion. motion.
When only one coordinate of When  two   coordinates When all three coordinates
the position of a body changes of the position of a body of the position of a body
with time then it is said to be changes with time then it changes  with time then it
moving one dimensionally. is said to be moving two  is said to be moving three
dimensionally. dimensionally.
Page 2


Physics Class XI
20
2.1 Motion in One Dimension : Position
Position of any point is completely expressed by two factors : Its distance  
 from the observer and its direction with respect to observer.
That is why position is characterised by a vector known as position vector.
Let point P is in a xy plane and its coordinates are (x, y). Then position  
 v ector of point will be  and if the point P is in a space and 
its coordinates are (x, y, z) then position vector can be expressed as 
2.2 Rest and Motion
If a body does not change its position as time passes with respect to frame 
of reference, it is said to be at rest.
And if a body changes its position as time passes with respect to frame 
of reference, it is said to be in motion.
Frame of Reference : It is a system to which a seet of coordinates are 
attached and with reference to which observer describes any event.
Rest and motion are relative terms. It depends upon the frame of references.
2.3 Types of Motion
      One dimensional    Two dimensional   Three dimensional
Motion of a body in a straight Motion of body in a plane Motion of body in a space
line is called one dimensional is called two dimensional is called three dimensional
motion. motion. motion.
When only one coordinate of When  two   coordinates When all three coordinates
the position of a body changes of the position of a body of the position of a body
with time then it is said to be changes with time then it changes  with time then it
moving one dimensionally. is said to be moving two  is said to be moving three
dimensionally. dimensionally.
e.g.,  Motion  of  car  on  a  e.g., Motion of car on a e.g., Motion of ?ying kite.
straight road. circular turn. Motion of ?ying insect.
Motion of freely falling body. Motion of billiards ball.
2.4 Distance and Displacement
(1) Distance : It is the actual path length covered by a moving particle in a 
given interval of time.
(i) Its a scalar quantity.
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(2) Displacement : Displacement is the change in position vector i.e., A 
vector joining initial to ?nal position.
(i) Displacement is a vector  quantity
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(iv) If are the displacements of a body then the total (net) 
displacement is the vector sum of the individuals. 
(3) Comparison between distance and displacement :
(i) Distance > Displacement.
(ii) For a moving particle distance can never be negative or zero while  
 displacement can be i.e., Distance > 0 but Displacement > = or < 0.
(iii) For motion between two points displacement is single valued while  
distance depends on actual path and so can have many values.
(iv) For a moving particle distance can never decrease with time while  
displacement can. Decrease in displacement with time means body  
is moving towards the initial position.
(v) In general magnitude of displacement is not equal to distance.  
However, it can be so if the motion is along a straight line without  
change in direction.
Page 3


Physics Class XI
20
2.1 Motion in One Dimension : Position
Position of any point is completely expressed by two factors : Its distance  
 from the observer and its direction with respect to observer.
That is why position is characterised by a vector known as position vector.
Let point P is in a xy plane and its coordinates are (x, y). Then position  
 v ector of point will be  and if the point P is in a space and 
its coordinates are (x, y, z) then position vector can be expressed as 
2.2 Rest and Motion
If a body does not change its position as time passes with respect to frame 
of reference, it is said to be at rest.
And if a body changes its position as time passes with respect to frame 
of reference, it is said to be in motion.
Frame of Reference : It is a system to which a seet of coordinates are 
attached and with reference to which observer describes any event.
Rest and motion are relative terms. It depends upon the frame of references.
2.3 Types of Motion
      One dimensional    Two dimensional   Three dimensional
Motion of a body in a straight Motion of body in a plane Motion of body in a space
line is called one dimensional is called two dimensional is called three dimensional
motion. motion. motion.
When only one coordinate of When  two   coordinates When all three coordinates
the position of a body changes of the position of a body of the position of a body
with time then it is said to be changes with time then it changes  with time then it
moving one dimensionally. is said to be moving two  is said to be moving three
dimensionally. dimensionally.
e.g.,  Motion  of  car  on  a  e.g., Motion of car on a e.g., Motion of ?ying kite.
straight road. circular turn. Motion of ?ying insect.
Motion of freely falling body. Motion of billiards ball.
2.4 Distance and Displacement
(1) Distance : It is the actual path length covered by a moving particle in a 
given interval of time.
(i) Its a scalar quantity.
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(2) Displacement : Displacement is the change in position vector i.e., A 
vector joining initial to ?nal position.
(i) Displacement is a vector  quantity
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(iv) If are the displacements of a body then the total (net) 
displacement is the vector sum of the individuals. 
(3) Comparison between distance and displacement :
(i) Distance > Displacement.
(ii) For a moving particle distance can never be negative or zero while  
 displacement can be i.e., Distance > 0 but Displacement > = or < 0.
(iii) For motion between two points displacement is single valued while  
distance depends on actual path and so can have many values.
(iv) For a moving particle distance can never decrease with time while  
displacement can. Decrease in displacement with time means body  
is moving towards the initial position.
(v) In general magnitude of displacement is not equal to distance.  
However, it can be so if the motion is along a straight line without  
change in direction.
2.5 Speed and Velocity
(1) Speed : Rate of distance covered with time is called speed.
(i) It is a scalar quantity having symbol v.
(ii) Dimension : [M
0
L
1
T
–1
]
(iii) Unit : metre/second (S.I.), cm/second (C. G. S.)
(iv) Types of speed :
(a) Uniform speed : When a particle covers equal distances in equal  
intervals of time, (no matter how small the intervals are) then it  
is said to be moving with uniform speed.
(b) Non-uniform (variable) speed : In non-uniform speed particle  
covers unequal distances in equal intervals of time.
(c) Average speed : The average speed of a particle for a given  
‘Interval of time’ is de?ned as the ratio of distance travelled to  
the time taken.
Average speed = ; v
av
 =
• Time average speed : When particle moves with different
uniform  speed ?
1
, ?
2
, ?
3
 .... etc. in different time intervals t
1
,t
2
,
t
3
, ... etc. respectively, its average speed over the total time of
journey is given as
v
av 
= = 
= 
Special case : When particle moves with speed v
1
 upto half time
of its total motion and in rest time it is moving with speed v
2
  then
v
av
 =
.
• Distance averaged speed : When a particle describes different
distances d
1
, d
2
, d
3
, .... with different time intervals t
1
, t
2
, t
3
, ....
with speeds v
1
, v
2
, v
3
, .... respectively then the speed of particle
averaged over the total distance can be given as 
 v
av 
= = 
Page 4


Physics Class XI
20
2.1 Motion in One Dimension : Position
Position of any point is completely expressed by two factors : Its distance  
 from the observer and its direction with respect to observer.
That is why position is characterised by a vector known as position vector.
Let point P is in a xy plane and its coordinates are (x, y). Then position  
 v ector of point will be  and if the point P is in a space and 
its coordinates are (x, y, z) then position vector can be expressed as 
2.2 Rest and Motion
If a body does not change its position as time passes with respect to frame 
of reference, it is said to be at rest.
And if a body changes its position as time passes with respect to frame 
of reference, it is said to be in motion.
Frame of Reference : It is a system to which a seet of coordinates are 
attached and with reference to which observer describes any event.
Rest and motion are relative terms. It depends upon the frame of references.
2.3 Types of Motion
      One dimensional    Two dimensional   Three dimensional
Motion of a body in a straight Motion of body in a plane Motion of body in a space
line is called one dimensional is called two dimensional is called three dimensional
motion. motion. motion.
When only one coordinate of When  two   coordinates When all three coordinates
the position of a body changes of the position of a body of the position of a body
with time then it is said to be changes with time then it changes  with time then it
moving one dimensionally. is said to be moving two  is said to be moving three
dimensionally. dimensionally.
e.g.,  Motion  of  car  on  a  e.g., Motion of car on a e.g., Motion of ?ying kite.
straight road. circular turn. Motion of ?ying insect.
Motion of freely falling body. Motion of billiards ball.
2.4 Distance and Displacement
(1) Distance : It is the actual path length covered by a moving particle in a 
given interval of time.
(i) Its a scalar quantity.
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(2) Displacement : Displacement is the change in position vector i.e., A 
vector joining initial to ?nal position.
(i) Displacement is a vector  quantity
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(iv) If are the displacements of a body then the total (net) 
displacement is the vector sum of the individuals. 
(3) Comparison between distance and displacement :
(i) Distance > Displacement.
(ii) For a moving particle distance can never be negative or zero while  
 displacement can be i.e., Distance > 0 but Displacement > = or < 0.
(iii) For motion between two points displacement is single valued while  
distance depends on actual path and so can have many values.
(iv) For a moving particle distance can never decrease with time while  
displacement can. Decrease in displacement with time means body  
is moving towards the initial position.
(v) In general magnitude of displacement is not equal to distance.  
However, it can be so if the motion is along a straight line without  
change in direction.
2.5 Speed and Velocity
(1) Speed : Rate of distance covered with time is called speed.
(i) It is a scalar quantity having symbol v.
(ii) Dimension : [M
0
L
1
T
–1
]
(iii) Unit : metre/second (S.I.), cm/second (C. G. S.)
(iv) Types of speed :
(a) Uniform speed : When a particle covers equal distances in equal  
intervals of time, (no matter how small the intervals are) then it  
is said to be moving with uniform speed.
(b) Non-uniform (variable) speed : In non-uniform speed particle  
covers unequal distances in equal intervals of time.
(c) Average speed : The average speed of a particle for a given  
‘Interval of time’ is de?ned as the ratio of distance travelled to  
the time taken.
Average speed = ; v
av
 =
• Time average speed : When particle moves with different
uniform  speed ?
1
, ?
2
, ?
3
 .... etc. in different time intervals t
1
,t
2
,
t
3
, ... etc. respectively, its average speed over the total time of
journey is given as
v
av 
= = 
= 
Special case : When particle moves with speed v
1
 upto half time
of its total motion and in rest time it is moving with speed v
2
  then
v
av
 =
.
• Distance averaged speed : When a particle describes different
distances d
1
, d
2
, d
3
, .... with different time intervals t
1
, t
2
, t
3
, ....
with speeds v
1
, v
2
, v
3
, .... respectively then the speed of particle
averaged over the total distance can be given as 
 v
av 
= = 
= 
(d) Instantaneous speed : It is the speed of a particle at particular  
instant. When we say ‘‘speed’’, it usually means instantaneous  
speed.
The instantaneous speed is average speed for in?nitesimally small time 
interval (i.e.?t ? 0). Thus
Instantaneous speed v = = 
(2) Velocity : Rate of change of position i.e.,  rate of displacement with time 
is called velocity.
(i) It is a scalar quantity having symbol v.
(ii) Dimension : [M
0
 L
1
T
–1
]
(iii) Unit : metre/second (S. I.), cm/second (C. G. S.)
(iv) Types
  (a) Uniform velocity : A particle is said to have uniform velocity,  
if magnitudes as well as direction of its velocity remains same  
and this is possible only when the particles moves in same  
straight line without reversing its direction.
  (b)  Non-uniform velocity : A particle is said to have non-uniform  
velocity, if either of magnitude or direction of velocity changes  
(or both changes).
  (c) Average velocity : It is de?ned as the ratio of displacement to  
time taken by the body
Average velocity =  = 
  (d) Instantaneous velocity : Instantaneous velocity is de?ned as  
rate of change of position vector of particles with time at a certain  
instant of time.
Instantaneous velocity = = 
Page 5


Physics Class XI
20
2.1 Motion in One Dimension : Position
Position of any point is completely expressed by two factors : Its distance  
 from the observer and its direction with respect to observer.
That is why position is characterised by a vector known as position vector.
Let point P is in a xy plane and its coordinates are (x, y). Then position  
 v ector of point will be  and if the point P is in a space and 
its coordinates are (x, y, z) then position vector can be expressed as 
2.2 Rest and Motion
If a body does not change its position as time passes with respect to frame 
of reference, it is said to be at rest.
And if a body changes its position as time passes with respect to frame 
of reference, it is said to be in motion.
Frame of Reference : It is a system to which a seet of coordinates are 
attached and with reference to which observer describes any event.
Rest and motion are relative terms. It depends upon the frame of references.
2.3 Types of Motion
      One dimensional    Two dimensional   Three dimensional
Motion of a body in a straight Motion of body in a plane Motion of body in a space
line is called one dimensional is called two dimensional is called three dimensional
motion. motion. motion.
When only one coordinate of When  two   coordinates When all three coordinates
the position of a body changes of the position of a body of the position of a body
with time then it is said to be changes with time then it changes  with time then it
moving one dimensionally. is said to be moving two  is said to be moving three
dimensionally. dimensionally.
e.g.,  Motion  of  car  on  a  e.g., Motion of car on a e.g., Motion of ?ying kite.
straight road. circular turn. Motion of ?ying insect.
Motion of freely falling body. Motion of billiards ball.
2.4 Distance and Displacement
(1) Distance : It is the actual path length covered by a moving particle in a 
given interval of time.
(i) Its a scalar quantity.
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(2) Displacement : Displacement is the change in position vector i.e., A 
vector joining initial to ?nal position.
(i) Displacement is a vector  quantity
(ii) Dimension : [M
0
 L
1
 T
0
]
(iii) Unit : metre (S. I.)
(iv) If are the displacements of a body then the total (net) 
displacement is the vector sum of the individuals. 
(3) Comparison between distance and displacement :
(i) Distance > Displacement.
(ii) For a moving particle distance can never be negative or zero while  
 displacement can be i.e., Distance > 0 but Displacement > = or < 0.
(iii) For motion between two points displacement is single valued while  
distance depends on actual path and so can have many values.
(iv) For a moving particle distance can never decrease with time while  
displacement can. Decrease in displacement with time means body  
is moving towards the initial position.
(v) In general magnitude of displacement is not equal to distance.  
However, it can be so if the motion is along a straight line without  
change in direction.
2.5 Speed and Velocity
(1) Speed : Rate of distance covered with time is called speed.
(i) It is a scalar quantity having symbol v.
(ii) Dimension : [M
0
L
1
T
–1
]
(iii) Unit : metre/second (S.I.), cm/second (C. G. S.)
(iv) Types of speed :
(a) Uniform speed : When a particle covers equal distances in equal  
intervals of time, (no matter how small the intervals are) then it  
is said to be moving with uniform speed.
(b) Non-uniform (variable) speed : In non-uniform speed particle  
covers unequal distances in equal intervals of time.
(c) Average speed : The average speed of a particle for a given  
‘Interval of time’ is de?ned as the ratio of distance travelled to  
the time taken.
Average speed = ; v
av
 =
• Time average speed : When particle moves with different
uniform  speed ?
1
, ?
2
, ?
3
 .... etc. in different time intervals t
1
,t
2
,
t
3
, ... etc. respectively, its average speed over the total time of
journey is given as
v
av 
= = 
= 
Special case : When particle moves with speed v
1
 upto half time
of its total motion and in rest time it is moving with speed v
2
  then
v
av
 =
.
• Distance averaged speed : When a particle describes different
distances d
1
, d
2
, d
3
, .... with different time intervals t
1
, t
2
, t
3
, ....
with speeds v
1
, v
2
, v
3
, .... respectively then the speed of particle
averaged over the total distance can be given as 
 v
av 
= = 
= 
(d) Instantaneous speed : It is the speed of a particle at particular  
instant. When we say ‘‘speed’’, it usually means instantaneous  
speed.
The instantaneous speed is average speed for in?nitesimally small time 
interval (i.e.?t ? 0). Thus
Instantaneous speed v = = 
(2) Velocity : Rate of change of position i.e.,  rate of displacement with time 
is called velocity.
(i) It is a scalar quantity having symbol v.
(ii) Dimension : [M
0
 L
1
T
–1
]
(iii) Unit : metre/second (S. I.), cm/second (C. G. S.)
(iv) Types
  (a) Uniform velocity : A particle is said to have uniform velocity,  
if magnitudes as well as direction of its velocity remains same  
and this is possible only when the particles moves in same  
straight line without reversing its direction.
  (b)  Non-uniform velocity : A particle is said to have non-uniform  
velocity, if either of magnitude or direction of velocity changes  
(or both changes).
  (c) Average velocity : It is de?ned as the ratio of displacement to  
time taken by the body
Average velocity =  = 
  (d) Instantaneous velocity : Instantaneous velocity is de?ned as  
rate of change of position vector of particles with time at a certain  
instant of time.
Instantaneous velocity = = 
(v) Comparison between instantaneous speed and instantaneous velocity
(a) Instantaneous velocity is always tangential to the path followed  
by the particle.
(b) A particle may have constant instantaneous speed but variable  
instantaneous velocity.
(c) The magnitude of instantaneous velocity is equal to the  
instantaneous speed.
(d) If a particle is moving with constant velocity then its average  
velocity and instantaneous velocity are always equal.
(e) If displacement is given as a function of time, then time derivative  
of displacement will give velocity.
(vi) Comparison between average speed and average velocity
(a) Average speed is scalar while average velocity is a vector both  
having same units (m/s) and dimensions [LT
–1
].
(b) Average speed or velocity depends on time interval over which it  
is de?ned.
(c) For a given time interval average velocity is single valued while  
average speed can have many values depending on path followed.
(d) If after motion body comes back to its initial position then =  
but v
av
 >  and ?nite as (?s > 0).
(e) For a moving body average speed can never be negative  
or zero (unless t ? 8) while average velocity can be i.e.,  
> 0 while = or < 0.
2.6 Acceleration
The time rate of change of velocity of an object is called acceleration of 
the object.
(1) It is a vector quantity. It’s direction is same as that of change in velocity 
(not of the velocity)
(2) There are three possible ways by which change in velocity may occur