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:

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