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Physics · MOTION IN A STRAIGHT LINE
हिन्दीThe position \( x \) of a particle moving along a straight line is related to time \( t \) by the relation \( t = \sqrt{x} + 3 \), where \( x \) is in meters and \( t \) is in seconds. Find the displacement of the particle from \( t = 0 \text{ s} \) to the moment when its velocity becomes zero.
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Correct answer · Option B
\( -9 \text{ m} \)
Explanation
Rearranging gives \( \sqrt{x} = t - 3 \implies x = (t - 3)^2 \). Velocity \( v = \frac{dx}{dt} = 2(t - 3) \). Velocity is zero at \( t = 3 \text{ s} \). Positions: \( x(0) = 9 \text{ m} \) and \( x(3) = 0 \text{ m} \). Displacement \( \Delta x = x(3) - x(0) = 0 - 9 = -9 \text{ m} \).
