Question

prove that s = ut + 1/2 at²​

Answer 1

refer to the attachment buddy

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Answer 2

Let OA = u

OD = AC = t

BD = v

So, BC = v - u

and v = u + at

The distance covered by the body having initial velocity u and final velocity v with acceleration a in time t is given by__

s = area of the trapezium OABD

= area of the rectangle OACD + area of triangle ABC

= (OA × OD) + 1/2 AC × BC

= u.t + 1/2 × t × (v - u)

s = ut + 1/2t . at [as v = u + at, then v - u = at]

Therefore,

s = ut + 1/2at ²