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A body falling freely from rest describes distances $S_{1}, S_{2} and S_{3}$ respectively in the $1^{st}, 2^{nd} and 3^{rd}$ seconds of its fall. The ratio $S_{1} : S_{2} : S_{3}$ is

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1 : 1 : 1

1 : 4 : 9

1 : 3 : 5

1 : 2 : 3

answer is B.

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Detailed Solution

$S_{1} = 0 + \frac{g}{2} (2 \times 1 - 1) S_{1} = \frac{g}{2} (1) Similarly, S_{2} = \frac{g}{2} (2 \times 2 - 1) = \frac{g}{2} (3) & S_{3} = \frac{g}{2} (2 \times 3 - 1) = \frac{g}{2} (5) ∴ S_{1} : S_{2} : S_{3} = 1 : 3 : 5$

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