Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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

24 metres

12 metres

5 metres

zero

Step-by-Step Solution

Rearrange the Equation: Isolate $x$ in the given relation $3t = \sqrt{3x} + 6$ . $\sqrt{3x} = 3t - 6$ Squaring both sides: $3x = (3t - 6)^2$ $3x = 9(t - 2)^2$ $x = 3(t - 2)^2$
Find Velocity ( $v$ ): Instantaneous velocity is the rate of change of displacement with respect to time, $v = \frac{dx}{dt}$ . Differentiating $x$ with respect to $t$ : $v = \frac{d}{dt}[3(t - 2)^2]$ $v = 3 \cdot 2(t - 2) \cdot 1$ $v = 6(t - 2)$ .
Condition for Zero Velocity: Set $v = 0$ . $6(t - 2) = 0 \implies t = 2 \text{ s}$ .
Calculate Displacement: Find the displacement $x$ at $t = 2 \text{ s}$ . Substitute $t = 2$ into the position equation: $x = 3(2 - 2)^2$ $x = 3(0)^2 = 0 \text{ metres}$ .

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