Equation of Motion
There are three important equations which are used to solve the problems about the motion of bodies. These equations show the relation between initial velocity, final velocity, acceleration, distance and time. These are known as equations of motion. It is necessary to mention that in these equations
- Motion will always be taken along straight line.
- Acceleration will be uniform.
- Although velocity, acceleration etc. are vector quantities but in these equations their magnitude will only be considered.
- Initial velocity will be taken as positive. Other quantities which are in the direction of initial velocity will be taken as positive and in the opposite direction will be taken as negative
Derivation
This derivation is based on the properties of a velocity-time graph for uniformly accelerated motion where the
This derivation is based on the properties of a velocity-time graph for uniformly accelerated motion where the
- slope of the graph represents the acceleration
- graph's area represents the displacement
1st Equation of Motion
Suppose a car is moving with initial velocity vi and after time t its velocity becomes vf. As the car moving with uniform acceleration therefore its acceleration ‘a’ will be equal to the average acceleration.
Since the acceleration is constant, the average acceleration is also the same as the instantaneous acceleration. From the definition of acceleration, the acceleration of a body is the rate of change of an object’s speed with time, we have
Suppose a car is moving with initial velocity vi and after time t its velocity becomes vf. As the car moving with uniform acceleration therefore its acceleration ‘a’ will be equal to the average acceleration.
Since the acceleration is constant, the average acceleration is also the same as the instantaneous acceleration. From the definition of acceleration, the acceleration of a body is the rate of change of an object’s speed with time, we have
By cross multiplication, we get
It is known as the
first equation of motion. It is the relation among vi, vf,
a and t. If we know any three
quantities, we can calculate the fourth quantity from this equation.
Thus, we see that 
are equivalent when the acceleration is constant.
2nd Equation of Motion
A body is moving with
initial velocity vi and
after a certain time t its velocity
becomes vf ,
then in order to calculate the total distance S covered in time t, we
can make use of the following method:
As, we know from first equation of motion 
, put this value in above equation, we get
, put this value in above equation, we get 
It is known as the
second equation of motion. It is the relation among S, vi, t and a. If we know any three
quantities, we can calculate the fourth quantity from this equation.
3rd Equation of Motion
A body is moving with initial velocity vi and after a certain time t its velocity becomes vf, then the distance S covered by it is given by
A body is moving with initial velocity vi and after a certain time t its velocity becomes vf, then the distance S covered by it is given by
By eliminating t from this equation and the first
equation of motion we can drive third equation of motion.
From first equation of
motion
By Putting the value of
t in eq. iii, we get
It is known as the third equation of motion. It
is the relation among a, S, vf and vi. If we know any three quantities, we can calculate
the fourth quantity from this equation.
Rotational equations of motion
The analogues of the above equations can be written for rotation:
The analogues of the above equations can be written for rotation:
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