Question

Derive formula for Velocity time relation, position time relation and position Velocity relation

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clear derivative ​

Answer 1

Answer:

your answer is in the attachment

Answer 2

☞︎︎︎ Derivation

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• Velocity time relation

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$\large \rm \mapsto \: \: a = \dfrac{v - u}{t}$

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$\large \rm \mapsto \: \: v - u = at$

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$\large \boxed{ \rm \mapsto \: \: v = u + at}$

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• Position time relation

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AOCB =

$\large \rm \: = sum \: of \: parallel \: sides \times \dfrac{1}{2} h$

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$\large \rm \implies \: s = (ao + bc) \dfrac{1}{2 } \times ad$

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$\large \rm \implies \: s = (u + v) \times \dfrac{1}{2 } \times t$

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• v = u + ar

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$\large \rm \implies \: s = (u + u + at) \dfrac{1}{2 } t$

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$\large \rm \implies \: s = (2u+ at) \dfrac{1}{2 } t$

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$\large \rm \therefore \boxed{\: \rm \: s = ut + \dfrac{at ^{2} }{2 } }$