Question

derive graphically the equations for positions time relation for an object travelling a distance s in time t under uniform acceleration

Answer 1

Hi, I am attatching a pic to make it easier.

We know that the area of a velocity - time graph is equal to its distance.
So, s = area of the graph
The graph can be broken down to 2 pieces - a rectangle and a triangle.
∴ s = area of the rectangle + area of the triangle
Area of the rectangle = l x b
                                   = u x t 
                                   = ut
Area of the triangle = (1/2)bh
                               = (1/2)(v-u)t               ( (v - u)/t = a. ∴ v - u = at)
                               = 1/2 at x t
                               = 1/2 at²                             
∴ s = area of the rectangle + area of the triangle
   s = ut + 1/2 at²

Hence Proved!

Hope it helps!