Question

3. Derive the equation for uniform accelerated motion for the displacement covered in
its nth second of its motion. (S = u + a (n - 1/2)) (AS)
A body leaving a certain point "O" moves with an a constant acceleration. At the endal​

Answer 1

Answer :-

Distance covered in nth second = Distance travelled in n sec - distance travelled in ( n - 1 ) sec.

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So, $\rm S_{nth} = S_n - S{(n-1)}$

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Substituting the value as t = n and t = ( n - 1 ) respectively in 2nd equation of motion -

$\rm S_{nth} = \big( un + \frac{1}{2} an^2 \big) - \big[ u ( n - 1 ) + \frac{1}{2} a ( n - 1 )^2 \big]$

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$\rm S_{nth} = \cancel{un} + \frac{1}{2} an^2 - \cancel{un} + u - \frac{1}{2}a ( n^2 - 2n + 1 )$

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$\rm S_{nth} = \frac{1}{2}an^2 + u - \frac{1}{2}a ( n^2 - 2n + 1 )$

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$\boxed{\rm S_{nth} = u + \frac{a}{2}(2n-1)}$