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  4. The work done by a force F =-5 x4 hat i N in displacing a body from, x=2 m to x=-2 m is

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Q. The work done by a force $F =-5 x^{4} \hat{ i } N$ in displacing a body from, $x=2 m$ to $x=-2 m$ is

AP EAMCETAP EAMCET 2019

Solution:

Given, force on the body, $F =-5 x^{4} \hat{ i } N$
Body is displacing from $x=2 m$ to $x=-2 m$.
Hence, the work done by a force in displacing a body,
$W=\int\limits_{x=2}^{x=-2} F \cdot d x$ or
$W=\int\limits_{x=2 m}^{x=-2}\left(-5 x^{4}\right) d x=(-5)\left[\frac{x^{5}}{5}\right]_{2}^{-2}$
$\Rightarrow =(-1)(-2)^{5}-(2)^{5}$
$ \Rightarrow W=64\, J $