A body is moving from rest under constant acc | vedclass

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Question

(A) Given that the body starts from rest,so initial velocity $u = 0$. Using the equation of motion $S = ut + \frac{1}{2}at^2$,we have: $S_1 = \frac{1}

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$S_1 + S_2$

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(A) Given that the body starts from rest,so initial velocity $u = 0$. Using the equation of motion $S = ut + \frac{1}{2}at^2$,we have: $S_1 = \frac{1}{2}a(p - 1)^2$ $S_2 = \frac{1}{2}ap^2$ Adding these two displacements: $S_1 + S_2 = \frac{1}{2}a(p^2 - 2p + 1) + \frac{1}{2}ap^2 = \frac{1}{2}a(2p^2 - 2p + 1)$ Now,the displacement in the $n^{th}$ second is given by $S_n = u + \frac{a}{2}(2n - 1)$. For $n = (p^2 - p + 1)$,the displacement is: $S_{(p^2 - p + 1)^{th}} = 0 + \frac{a}{2}[2(p^2 - p + 1) - 1] = \frac{a}{2}[2p^2 - 2p + 2 - 1] = \frac{a}{2}(2p^2 - 2p + 1)$. Comparing the results,we find that the displacement in the $(p^2 - p + 1)^{th}$ second is equal to $S_1 + S_2$.

Column-$I$	Column-$II$
$(1)$ Velocity-time relation	$(a)$ $v = v_0 + at$
$(2)$ Velocity-displacement relation	$(b)$ $S = v_0t + \frac{1}{2}at^2$
	$(c)$ $v^2 = v_0^2 + 2as$

$A$ body is moving from rest under constant acceleration. Let $S_1$ be the displacement in the first $(p - 1) \ s$ and $S_2$ be the displacement in the first $p \ s$. The displacement in the $(p^2 - p + 1)^{th} \ s$ will be:

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Column-$I$ Column-$II$

$(1)$ Velocity-time relation $(a)$ $v = v_0 + at$

$(2)$ Velocity-displacement relation $(b)$ $S = v_0t + \frac{1}{2}at^2$

$(c)$ $v^2 = v_0^2 + 2as$

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