Derive the relation `s = ut + (1)/(2) at ^(2) ` for uniformly accelerated motion along a straight line.

Explanation

Let `x _(0) ` is position of particle at t =0 and x is position at time t.
distance travelled in time t Area under OPQS region
= Area of rectangle OPRS + Area of triangle PQR
`= (PQ xx RS) + (1)/(2) (QR xx PR)`
From figure `PR = timplies RS = u`
`QR =v - u`
`x -x _(0) = ut + (1)/(2) (v - u) ,t ( because v - u = at)`
`x -x _(0)= ut + (1)/(2 ) at ^(2)`
s = distance covered `=x - x_(0) = ut + (1)/(2) at ^(2).`