In this article, we will derive the second equation of motion by graphical method.

### Formula for the second equation of motion

First equation of motion is given by the relation

$s=ut+\frac{1}{2}at^2$

Where

$v$= final velocity

$u$= initial velocity

$a$= acceleration

$s$= displacement of the object

$t$= time taken

Note: - This equation along with other kinematics equations of motion are valid for objects moving with uniform acceleration.

## Derivation of the 2nd equation of motion by graphical method:

To derive the 2nd equation of motion we will make the following assumptions

* Object under consideration is moving with acceleration \(a\,\, m/s^2\)

* At time \(t=0\) object have some initial velocity. Let’s denote it by \(u\,\, m/s\)

* At time \(ts\) object have some final velocity. Let’s denote it by \(v\,\, m/s\)

* Total displacement of the object in time \(t\) seconds is \(s\) meters.

Object is moving with a uniform acceleration “a” along a straight line. The initial and final velocities of the object at time \(t = 0\) and \(t = t\,\, s\) are \(u\) and \(v\) respectively. During time \(t\), let \(s\) be the total displacement of the object.

Figure given below show the velocity-time graph for the object whose initial velocity is \(u\) at time \(t=0\) and velocity \(v\) at time \(t\).

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