A force acts on a particle in the -direction, where is in newton and is in meter. The work done by this force during a displacement from = 0 to = 4 m, is __________ J. [2023]

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Solution

Q.
A force $\vec{F} = (2 + 3 x) \hat{i}$ acts on a particle in the $x$ -direction, where $F$ is in newton and $x$ is in meter. The work done by this force during a displacement from $x$ = 0 to $x$ = 4 m, is __________ J. [2023]

Ans.
(32)

$W = \int_{2}^{4} (2 + 3 x) d x$ $= {[2 x + \frac{3 x^{2}}{2}]}_{0}^{4} = 8 + 3 \times 8 = 32 J$

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