derivation - equation 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: