1. Tardigrade
  2. Question
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  4. A position-dependent force F=3 x2-2 x+7 acts on a body of mass 7 kg and displaces it from x=0 m to x=5 m. The work done on the body is x' joule. If both F and x are measured in SI units, the value of x' is

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Q. A position-dependent force $F=3 x^{2}-2 x+7$ acts on a body of mass $7 \,kg$ and displaces it from $x=0\, m$ to $x=5 \,m$. The work done on the body is $x^{'}$ joule. If both $F$ and $x$ are measured in $SI$ units, the value of $x^{'}$ is

Work, Energy and Power

Solution:

This is the case of work done by a variable force
$W=\int\limits_{0}^{5}\left(3 x^{2}-2 x+7\right) d x$
$W=\left|x^{3}+x^{2}+7 x\right|_{0}^{5} $
or $W=(5 \times 5 \times 5-5 \times 5+7 \times 5)$
Or $W=(125-25+35)=135\, J$