Question

show that s=1/2 at^2 for uniform acceleration motion by any method​

Answer 1

Solution :

$\large\sf Average \: velocity = \dfrac{u + v}{2}$

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$\large\sf Distance = Average \: velocity \times time$

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$\large\implies\sf s = \dfrac{u + v}{2} \times t$

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$\large\sf Putting \: v = u + at$

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$\large\implies\sf s = \bigg(\dfrac{u + u + at}{2}\bigg)\times t$

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$\large\implies \sf s = \dfrac{2ut + a {t}^{2} }{2}$

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$\large \implies \boxed{\sf s = ut + \frac{1}{2} {at}^{2}}$