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Question

(B) Given that the body starts from rest,the initial velocity $u = 0$. The displacement $S$ covered in time $t$ with constant acceleration $a$ is give

Vedclass · Accepted Answer

$\sqrt{2p^2-2p+1} \ s$

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(B) Given that the body starts from rest,the initial velocity $u = 0$. The displacement $S$ covered in time $t$ with constant acceleration $a$ is given by $S = \frac{1}{2}at^2$.For the first $(p-1)$ seconds,the displacement is $S_1 = \frac{1}{2}a(p-1)^2$.For the first $p$ seconds,the displacement is $S_2 = \frac{1}{2}ap^2$.We need to find the time $t$ such that the total displacement is $S_1 + S_2 = \frac{1}{2}at^2$.Substituting the expressions for $S_1$ and $S_2$:$\frac{1}{2}a(p-1)^2 + \frac{1}{2}ap^2 = \frac{1}{2}at^2$Dividing both sides by $\frac{1}{2}a$:$(p-1)^2 + p^2 = t^2$$p^2 - 2p + 1 + p^2 = t^2$$2p^2 - 2p + 1 = t^2$$t = \sqrt{2p^2 - 2p + 1} \ s$.

$A$ body starts moving from rest with constant acceleration. It covers a displacement $S_1$ in the first $(p-1)$ seconds and $S_2$ in the first $p$ seconds. The total displacement $S_1+S_2$ will be covered in time:

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