Work Energy Theorem

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Question

A particle is at rest at the origin. Mass of the particle is 2 kg. It is displaced by 4m along the x-axis under the influence of a force $\vec{F} = (2 x) \hat{i} N$ , then find velocity of the particle is

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Solution

$W = \int_{0}^{4} \vec{F} . d \vec{x} = \int_{0}^{4} (2 x \hat{i}) . (d x \hat{i}) = 2 {[\frac{x^{2}}{2}]}_{0}^{4} J$
$\Rightarrow W = 16 J$
By work energy theorem, $\frac{1}{2} \times 2 \times V^{2} - 0 = 16 \Rightarrow V = 4 m / s$

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