Important Kinematics Formulas for JEE and NEET

 Page 1


Motion in a straight line class 11 formulas
Distance – The total length that is travelled between different positions.
Displacement – Distance between two points in a particular direction.
Formula :- 
 Displacement
 final position
 initial position
Speed – the total distance covered divided by the time taken to cover that distance.
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Velocity – the displacement divided by the time it takes for the displacement
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Average Speed – the total distance covered divided by the time taken to cover that distance
Formula :- 
Body covering different distances with different speeds
If the body covers the first half of the total distance with speed  and the second half with the speed 
, then the average speed is given by
In this case, the average speed is the harmonic mean of individual speeds.
The body is moving at different speeds in different time intervals and then
Total distance travelled 
Total time taken 
If  then,
In this case, the average speed is the arithmetic mean of the individual speeds.
Average Velocity – the total displacement covered divided by the time taken for that displacement
?x = x
f
- x
i
?x ?
x
f
?
x
i
?
Speed =
Total Distance Covered
Time Taken
m/s Km/hr mph
[M
0
LT
-1
]
V elocity =
Displacement
Time
m/s Km/hr mph
[M
0
LT
-1
]
Average Speed = =
Total Distance Covered
Time Taken
?x
?t
¯ v = =
s
1
+ s
2
+ s
3
+ … .
t
1
+ t
2
+ t
3
+ … .
s
1
+ s
2
+ s
3
+ … .
+ + + … . .
s
1
v
1
s
2
v
2
s
3
v
3
v
1
v
2
¯ v =
2v
1
v
2
v
1
+ v
2
= v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
= t
1
+ t
2
+ t
3
+ … .
¯ v =
v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
t
1
+ t
2
+ t
3
+ … .
t
1
= t
2
= t
3
= … . = t
n
= t
¯ v = =
(v
1
+ v
2
+ v
3
+ … . )t
nt
(v
1
+ v
2
+ v
3
+ … . )
n
             
Page 2


Motion in a straight line class 11 formulas
Distance – The total length that is travelled between different positions.
Displacement – Distance between two points in a particular direction.
Formula :- 
 Displacement
 final position
 initial position
Speed – the total distance covered divided by the time taken to cover that distance.
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Velocity – the displacement divided by the time it takes for the displacement
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Average Speed – the total distance covered divided by the time taken to cover that distance
Formula :- 
Body covering different distances with different speeds
If the body covers the first half of the total distance with speed  and the second half with the speed 
, then the average speed is given by
In this case, the average speed is the harmonic mean of individual speeds.
The body is moving at different speeds in different time intervals and then
Total distance travelled 
Total time taken 
If  then,
In this case, the average speed is the arithmetic mean of the individual speeds.
Average Velocity – the total displacement covered divided by the time taken for that displacement
?x = x
f
- x
i
?x ?
x
f
?
x
i
?
Speed =
Total Distance Covered
Time Taken
m/s Km/hr mph
[M
0
LT
-1
]
V elocity =
Displacement
Time
m/s Km/hr mph
[M
0
LT
-1
]
Average Speed = =
Total Distance Covered
Time Taken
?x
?t
¯ v = =
s
1
+ s
2
+ s
3
+ … .
t
1
+ t
2
+ t
3
+ … .
s
1
+ s
2
+ s
3
+ … .
+ + + … . .
s
1
v
1
s
2
v
2
s
3
v
3
v
1
v
2
¯ v =
2v
1
v
2
v
1
+ v
2
= v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
= t
1
+ t
2
+ t
3
+ … .
¯ v =
v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
t
1
+ t
2
+ t
3
+ … .
t
1
= t
2
= t
3
= … . = t
n
= t
¯ v = =
(v
1
+ v
2
+ v
3
+ … . )t
nt
(v
1
+ v
2
+ v
3
+ … . )
n
             
Formula :- 
Finding position from velocity – 
  
Instantaneous Velocity – is defined as the velocity of an object at a particular instant of time.
Formula :- 
Instantaneous Speed – is defined as the speed of an object at a particular instant of time. It is the
absolute value of instantaneous velocity.
Formula :- 
Acceleration – The rate of change of velocity is called acceleration.
Formula :- 
Instantaneous acceleration – acceleration of a particle at a particular instant of time
Formula :- 
Equations of motion with constant acceleration
First Equation of motion – finding velocity from acceleration – 
Second Equation of motion – finding position from velocity and acceleration – 
Third Equation of motion – finding velocity from distance and acceleration – 
Equation for finding distance travelled in  second of object’s journey – 
Average Velocity = or, ¯ v =
Displacement
Time Taken
? ? x
?t
x = x
0
+ ¯ vt
v(t) =
dx(t)
dt
Instantaneous speed = |v(t)|
a = =
? ? v
?t
v
f
-v
i
t
f
-t
i
a = lim
??0
=
?v
?t
dv
dt
v = v
0
+ at
x = x
0
+ v
0
t + at
2 1
2
v
2
= v
2
0
+ 2a(x– x
0
)
n
th
S
n
= u + a(n - )
1
2
             
Page 3


Motion in a straight line class 11 formulas
Distance – The total length that is travelled between different positions.
Displacement – Distance between two points in a particular direction.
Formula :- 
 Displacement
 final position
 initial position
Speed – the total distance covered divided by the time taken to cover that distance.
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Velocity – the displacement divided by the time it takes for the displacement
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Average Speed – the total distance covered divided by the time taken to cover that distance
Formula :- 
Body covering different distances with different speeds
If the body covers the first half of the total distance with speed  and the second half with the speed 
, then the average speed is given by
In this case, the average speed is the harmonic mean of individual speeds.
The body is moving at different speeds in different time intervals and then
Total distance travelled 
Total time taken 
If  then,
In this case, the average speed is the arithmetic mean of the individual speeds.
Average Velocity – the total displacement covered divided by the time taken for that displacement
?x = x
f
- x
i
?x ?
x
f
?
x
i
?
Speed =
Total Distance Covered
Time Taken
m/s Km/hr mph
[M
0
LT
-1
]
V elocity =
Displacement
Time
m/s Km/hr mph
[M
0
LT
-1
]
Average Speed = =
Total Distance Covered
Time Taken
?x
?t
¯ v = =
s
1
+ s
2
+ s
3
+ … .
t
1
+ t
2
+ t
3
+ … .
s
1
+ s
2
+ s
3
+ … .
+ + + … . .
s
1
v
1
s
2
v
2
s
3
v
3
v
1
v
2
¯ v =
2v
1
v
2
v
1
+ v
2
= v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
= t
1
+ t
2
+ t
3
+ … .
¯ v =
v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
t
1
+ t
2
+ t
3
+ … .
t
1
= t
2
= t
3
= … . = t
n
= t
¯ v = =
(v
1
+ v
2
+ v
3
+ … . )t
nt
(v
1
+ v
2
+ v
3
+ … . )
n
             
Formula :- 
Finding position from velocity – 
  
Instantaneous Velocity – is defined as the velocity of an object at a particular instant of time.
Formula :- 
Instantaneous Speed – is defined as the speed of an object at a particular instant of time. It is the
absolute value of instantaneous velocity.
Formula :- 
Acceleration – The rate of change of velocity is called acceleration.
Formula :- 
Instantaneous acceleration – acceleration of a particle at a particular instant of time
Formula :- 
Equations of motion with constant acceleration
First Equation of motion – finding velocity from acceleration – 
Second Equation of motion – finding position from velocity and acceleration – 
Third Equation of motion – finding velocity from distance and acceleration – 
Equation for finding distance travelled in  second of object’s journey – 
Average Velocity = or, ¯ v =
Displacement
Time Taken
? ? x
?t
x = x
0
+ ¯ vt
v(t) =
dx(t)
dt
Instantaneous speed = |v(t)|
a = =
? ? v
?t
v
f
-v
i
t
f
-t
i
a = lim
??0
=
?v
?t
dv
dt
v = v
0
+ at
x = x
0
+ v
0
t + at
2 1
2
v
2
= v
2
0
+ 2a(x– x
0
)
n
th
S
n
= u + a(n - )
1
2
             
VARIOUS GRAPHS RELATED TO MOTION                                                        
 
DISPLACEMENT-TIME GRAPH 
In this graph time is plotted on x-axis and displacement on y-axis. 
? For a stationary body (v = 0) the time-displacement graph is a straight line parallel to 
time axis. 
 
? When the velocity of a body is constant then time-displacement graph will be an oblique 
straight line. Greater the slope of the straight line, higher will be the velocity. 
 
? If the velocity of a body is not constant then the time-displacement curve is a zig-zag curve. 
 
Page 4


Motion in a straight line class 11 formulas
Distance – The total length that is travelled between different positions.
Displacement – Distance between two points in a particular direction.
Formula :- 
 Displacement
 final position
 initial position
Speed – the total distance covered divided by the time taken to cover that distance.
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Velocity – the displacement divided by the time it takes for the displacement
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Average Speed – the total distance covered divided by the time taken to cover that distance
Formula :- 
Body covering different distances with different speeds
If the body covers the first half of the total distance with speed  and the second half with the speed 
, then the average speed is given by
In this case, the average speed is the harmonic mean of individual speeds.
The body is moving at different speeds in different time intervals and then
Total distance travelled 
Total time taken 
If  then,
In this case, the average speed is the arithmetic mean of the individual speeds.
Average Velocity – the total displacement covered divided by the time taken for that displacement
?x = x
f
- x
i
?x ?
x
f
?
x
i
?
Speed =
Total Distance Covered
Time Taken
m/s Km/hr mph
[M
0
LT
-1
]
V elocity =
Displacement
Time
m/s Km/hr mph
[M
0
LT
-1
]
Average Speed = =
Total Distance Covered
Time Taken
?x
?t
¯ v = =
s
1
+ s
2
+ s
3
+ … .
t
1
+ t
2
+ t
3
+ … .
s
1
+ s
2
+ s
3
+ … .
+ + + … . .
s
1
v
1
s
2
v
2
s
3
v
3
v
1
v
2
¯ v =
2v
1
v
2
v
1
+ v
2
= v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
= t
1
+ t
2
+ t
3
+ … .
¯ v =
v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
t
1
+ t
2
+ t
3
+ … .
t
1
= t
2
= t
3
= … . = t
n
= t
¯ v = =
(v
1
+ v
2
+ v
3
+ … . )t
nt
(v
1
+ v
2
+ v
3
+ … . )
n
             
Formula :- 
Finding position from velocity – 
  
Instantaneous Velocity – is defined as the velocity of an object at a particular instant of time.
Formula :- 
Instantaneous Speed – is defined as the speed of an object at a particular instant of time. It is the
absolute value of instantaneous velocity.
Formula :- 
Acceleration – The rate of change of velocity is called acceleration.
Formula :- 
Instantaneous acceleration – acceleration of a particle at a particular instant of time
Formula :- 
Equations of motion with constant acceleration
First Equation of motion – finding velocity from acceleration – 
Second Equation of motion – finding position from velocity and acceleration – 
Third Equation of motion – finding velocity from distance and acceleration – 
Equation for finding distance travelled in  second of object’s journey – 
Average Velocity = or, ¯ v =
Displacement
Time Taken
? ? x
?t
x = x
0
+ ¯ vt
v(t) =
dx(t)
dt
Instantaneous speed = |v(t)|
a = =
? ? v
?t
v
f
-v
i
t
f
-t
i
a = lim
??0
=
?v
?t
dv
dt
v = v
0
+ at
x = x
0
+ v
0
t + at
2 1
2
v
2
= v
2
0
+ 2a(x– x
0
)
n
th
S
n
= u + a(n - )
1
2
             
VARIOUS GRAPHS RELATED TO MOTION                                                        
 
DISPLACEMENT-TIME GRAPH 
In this graph time is plotted on x-axis and displacement on y-axis. 
? For a stationary body (v = 0) the time-displacement graph is a straight line parallel to 
time axis. 
 
? When the velocity of a body is constant then time-displacement graph will be an oblique 
straight line. Greater the slope of the straight line, higher will be the velocity. 
 
? If the velocity of a body is not constant then the time-displacement curve is a zig-zag curve. 
 
? For an accelerated motion the slope of time-displacement curve increases with time while for 
decelerated motion it decreases with time. 
 
? When the particle returns towards the point of reference then the time-displacement line 
makes an angle ? > 90° with the time axis. 
 
VELOCITY-TIME GRAPH 
In this curve time is plotted along x-axis and velocity is plotted along y-axis. 
? When the velocity of the particle is constant or acceleration is zero. 
 
? When the particle is moving with a constant acceleration and its initial velocity is zero. 
Page 5


Motion in a straight line class 11 formulas
Distance – The total length that is travelled between different positions.
Displacement – Distance between two points in a particular direction.
Formula :- 
 Displacement
 final position
 initial position
Speed – the total distance covered divided by the time taken to cover that distance.
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Velocity – the displacement divided by the time it takes for the displacement
Formula :- 
Unit – ,  or (mile per hour)
Dimensions – 
Average Speed – the total distance covered divided by the time taken to cover that distance
Formula :- 
Body covering different distances with different speeds
If the body covers the first half of the total distance with speed  and the second half with the speed 
, then the average speed is given by
In this case, the average speed is the harmonic mean of individual speeds.
The body is moving at different speeds in different time intervals and then
Total distance travelled 
Total time taken 
If  then,
In this case, the average speed is the arithmetic mean of the individual speeds.
Average Velocity – the total displacement covered divided by the time taken for that displacement
?x = x
f
- x
i
?x ?
x
f
?
x
i
?
Speed =
Total Distance Covered
Time Taken
m/s Km/hr mph
[M
0
LT
-1
]
V elocity =
Displacement
Time
m/s Km/hr mph
[M
0
LT
-1
]
Average Speed = =
Total Distance Covered
Time Taken
?x
?t
¯ v = =
s
1
+ s
2
+ s
3
+ … .
t
1
+ t
2
+ t
3
+ … .
s
1
+ s
2
+ s
3
+ … .
+ + + … . .
s
1
v
1
s
2
v
2
s
3
v
3
v
1
v
2
¯ v =
2v
1
v
2
v
1
+ v
2
= v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
= t
1
+ t
2
+ t
3
+ … .
¯ v =
v
1
t
1
+ v
2
t
2
+ v
3
t
3
+ … .
t
1
+ t
2
+ t
3
+ … .
t
1
= t
2
= t
3
= … . = t
n
= t
¯ v = =
(v
1
+ v
2
+ v
3
+ … . )t
nt
(v
1
+ v
2
+ v
3
+ … . )
n
             
Formula :- 
Finding position from velocity – 
  
Instantaneous Velocity – is defined as the velocity of an object at a particular instant of time.
Formula :- 
Instantaneous Speed – is defined as the speed of an object at a particular instant of time. It is the
absolute value of instantaneous velocity.
Formula :- 
Acceleration – The rate of change of velocity is called acceleration.
Formula :- 
Instantaneous acceleration – acceleration of a particle at a particular instant of time
Formula :- 
Equations of motion with constant acceleration
First Equation of motion – finding velocity from acceleration – 
Second Equation of motion – finding position from velocity and acceleration – 
Third Equation of motion – finding velocity from distance and acceleration – 
Equation for finding distance travelled in  second of object’s journey – 
Average Velocity = or, ¯ v =
Displacement
Time Taken
? ? x
?t
x = x
0
+ ¯ vt
v(t) =
dx(t)
dt
Instantaneous speed = |v(t)|
a = =
? ? v
?t
v
f
-v
i
t
f
-t
i
a = lim
??0
=
?v
?t
dv
dt
v = v
0
+ at
x = x
0
+ v
0
t + at
2 1
2
v
2
= v
2
0
+ 2a(x– x
0
)
n
th
S
n
= u + a(n - )
1
2
             
VARIOUS GRAPHS RELATED TO MOTION                                                        
 
DISPLACEMENT-TIME GRAPH 
In this graph time is plotted on x-axis and displacement on y-axis. 
? For a stationary body (v = 0) the time-displacement graph is a straight line parallel to 
time axis. 
 
? When the velocity of a body is constant then time-displacement graph will be an oblique 
straight line. Greater the slope of the straight line, higher will be the velocity. 
 
? If the velocity of a body is not constant then the time-displacement curve is a zig-zag curve. 
 
? For an accelerated motion the slope of time-displacement curve increases with time while for 
decelerated motion it decreases with time. 
 
? When the particle returns towards the point of reference then the time-displacement line 
makes an angle ? > 90° with the time axis. 
 
VELOCITY-TIME GRAPH 
In this curve time is plotted along x-axis and velocity is plotted along y-axis. 
? When the velocity of the particle is constant or acceleration is zero. 
 
? When the particle is moving with a constant acceleration and its initial velocity is zero. 
 
? When the particle is moving with constant retardation. 
 
? When the particle moves with non-uniform acceleration and its initial velocity is zero. 
 
? When the acceleration decreases and increases. 
 
? The total area enclosed by the time - velocity curve represents the distance travelled by a 
body.