Please explain the derivation of the equations of motion by graphical method.

Here is the derivation of the equations of motion by graphical method. Follow the graph:

Let us suppose that * v *_{ 0 }is the initial velocity of the particle, at time t = 0, and * v *be the velocity of the particle at t = * t. *

The acceleration * a *of the particle can be written as,

This is the 1 ^{ st }kinematic equations for uniformly accelerated motion.

Suppose, the particle travels a distance * x *in the time * t *.

The area of blue colored part gives the distance covered * x *.

So,

This is the 2 ^{ nd }equation.

Now, for the 3 ^{ rd }equation we shall modify the equation:

The area of blue colored part gives the distance covered * x *.

So,

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