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
             
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