Question

Draw velocity time graph for an uniformly accelerated object. Derive s = ut +1/2 at^2

Answer 1

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Here is ur answer !!
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Ur answer is in pictures dear
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HAPPY RAKSHABANDHAN

Answer 2

Displacement of the particle in time taken (t)

S = Area under the velocity time graph

S = Ar(OABC) Picture Attached Below.

S = ar rectangle(AODC) + Area triangle ADB

$S = OAxOC + \frac{1}{2} ADxBD$

$S = ut + \frac{1}{2} (AD)x(\frac{ADxDB}{AD} )\\\\\\\\S = ut + \frac{1}{2} (AD)^{2} x (\frac{DB}{AD})$

$S = ut + \frac{1}{2} (t)^{2}\:x\:(a)\:\:\:[tan\:theta = \frac{BD}{AD} ]\\\\\\S = ut + \frac{1}{2} at^{2}$