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

$$S_1 = \frac{1}{2}a(p-1)^2$$, $$S_2 = \frac{1}{2}ap^2$$.

$$S_1 + S_2 = \frac{a}{2}[(p-1)^2 + p^2] = \frac{a}{2}(2p^2 - 2p + 1)$$

If this equals $$\frac{1}{2}at^2$$: $$t^2 = 2p^2 - 2p + 1$$, $$t = \sqrt{2p^2-2p+1}$$.

The answer corresponds to Option (2).

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