Question

derive the equation for velocity time relation (v=u+at) by graphical method

Answer 1

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,