Question

using a time velocity graph of an uniform accelerated motion,derive the equation of S = ut+1/2at^2 where every letter usual meaning​

Answer 1

$hope \: it \: is \: useful \: for \: u$

Answer 2

S = ut+1/2at²

Here is a link for graph : https://bit.ly/2NQmphS

Here, OA = u

BD = v

OD = t

BC = (v-u)

We know that area of trapezium (S) = 1/2×(sum of parallel sides)×(distance between parallel sides)

S = 1/2×(OA+BD)×(OD)

S = 1/2× (u+v)×t

We know that v = u+at

So,

S = 1/2×(u+u+at)×t

S = 1/2×(2u+at)×t

S = 1/2×2u×t+1/2×at×t

S = ut+1/2at²

There you have it!