Question: The relation $3t = \sqrt{3x} + 6$ describes the displacement of a particle in one direction where ...

Question

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

Answer 1

Solution

$3t = \sqrt{3x} + 6$ ⇒ $\sqrt{3x} = (3t - 6)$ ⇒ $3x = (3t - 6)^{2}$

⇒ $x = 3t^{2} - 12t + 12$

∴ v = $\frac{dx}{dt} = \frac{d}{dt}(3t^{2} - 12t + 12) = 6t - 12$

If velocity = 0 then, $6t - 12 = 0$ $\Rightarrow t = 2sec$

Hence at t = 2, x = 3(2)² – 12 (2) + 12 = 0 metres.

Question: The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where ...

Solution