The relation $3 t = \sqrt{3 x} + 6$ describes the position of a particle in one direction where x is in metres and t in sec. The displacement, when velocity is zero, is

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5 metres

12 metres

Zero

24 metres

answer is B.

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Detailed Solution

$3 t = \sqrt{3 x} + 6 - - - (1)$

$\sqrt{3 x} = 3 t - 6; \sqrt{3 x} = 3 (t - 2)$

Squaring on both sides x = 3(t - 2)²

$\begin{array}{l} \frac{dx}{dt} = 3 (t^{2} + 4 - 4 t) \\ V = 3 (2 t - 4); v = 0; t = 2 \sec \\ S = |x_{f} - x_{i}| \\ = |3 [(2)^{2} + 4 - 4 (2) - (0)^{2} - 4 - 4 (0)]| \end{array}$

= 3 x 4 = 12m

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