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Acceleration of a particle of mass 2 kg moving along x-axis is $a = 2 x m / s^{2}$ where $x$ is in metre. Then work done by the force acting on the particle in displacing it from $x$ = 1 m to $x$ = 2 m is

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16 J

6 J

12 J

8 J

answer is D.

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Detailed Solution

$F = m a = 2 \times 2 x = 4 x$

$∴ W = \int_{1}^{2} F d x = 4 \int_{1}^{2} x d x = {[\frac{4 x^{2}}{2}]}_{1}^{2} = 2 (2^{2} - 1^{2}) J = 6 J$

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