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Physics · MOTION IN A STRAIGHT LINE
हिन्दीA body starting from rest moves with constant acceleration \( a \). If the time taken by the body to cover successive equal distance segments \( S \) are \( t_1, t_2, t_3 \dots \), then the ratio \( t_1 : t_2 : t_3 \) is:
Correct answer · Option 1
\( 1 : (\sqrt{2}-1) : (\sqrt{3}-\sqrt{2}) \)
Explanation
Distance \( nS = \frac{1}{2} a T_n^2 \implies T_n = \sqrt{\frac{2nS}{a}} = \sqrt{n} t_1 \). Thus \( t_1 = t_1 \), \( t_2 = T_2 - T_1 = (\sqrt{2}-1)t_1 \), and \( t_3 = T_3 - T_2 = (\sqrt{3}-\sqrt{2})t_1 \).
