Correct Answer: Option C

Explanation

Given \( a_X = 2a_Y \) and both start from rest covering the same distance \( s \):

For X:
\(s = a_Y t_X^2\)

For Y:
\(s = \frac{1}{2} a_Y t_Y^2\)

Setting them equal:
\(a_Y t_X^2 = \frac{1}{2} a_Y t_Y^2 \implies t_X^2 = \frac{1}{2} t_Y^2\)

Thus: \(\frac{t_X}{t_Y} = \frac{1}{\sqrt{2}} \quad \Rightarrow \quad \frac{1}{\sqrt{2}}\)

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