Q 11-02-012NEETJEE MainEAMCET 1993 (Engineering)Easy
A particle starts moving from rest under uniform acceleration. It travels a distance $x$ in the first two seconds and a distance $y$ in the next two seconds. If $y = nx$, then $n =$
Answer: (C) $3$
Starting from rest, $s = \dfrac{1}{2}at^2$.
Distance in the first $2$ s: $x = \dfrac{1}{2}a(2)^2 = 2a$.
Distance in the first $4$ s: $\dfrac{1}{2}a(4)^2 = 8a$, so in the next $2$ s: $y = 8a - 2a = 6a$.
$$n = \frac{y}{x} = \frac{6a}{2a} = 3$$
Shortcut: from rest, distances in equal successive intervals are in the ratio $1 : 3 : 5 : \dots$
Solution by Sreeraj P, M.Sc Physics