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An-object-constrained-to-move-along-the-x-axis-is-acted-upon-by-a-force-F-x-where-a-5N-m-b-2N-m-F-x-ax-bx-2-The-object-is-observed-to-proceed-directly-from-x-1m-to-x-3m-How-much-work-was-done-b




Question Number 25307 by NECx last updated on 08/Dec/17
An object constrained to move  along the x-axis is acted upon by  a force F(x) where a=5N/m,  b=−2N/m. F(x)=ax+bx^2   The object is observed to proceed  directly from x=1m to x=3m.  How much work was done by the  object by the force?Does the  process of integration take into  account the fact that the force  F(x) changes sign in interval.
$${An}\:{object}\:{constrained}\:{to}\:{move} \\ $$$${along}\:{the}\:{x}-{axis}\:{is}\:{acted}\:{upon}\:{by} \\ $$$${a}\:{force}\:{F}\left({x}\right)\:{where}\:{a}=\mathrm{5}{N}/{m}, \\ $$$${b}=−\mathrm{2}{N}/{m}.\:{F}\left({x}\right)={ax}+{bx}^{\mathrm{2}} \\ $$$${The}\:{object}\:{is}\:{observed}\:{to}\:{proceed} \\ $$$${directly}\:{from}\:{x}=\mathrm{1}{m}\:{to}\:{x}=\mathrm{3}{m}. \\ $$$${How}\:{much}\:{work}\:{was}\:{done}\:{by}\:{the} \\ $$$${object}\:{by}\:{the}\:{force}?{Does}\:{the} \\ $$$${process}\:{of}\:{integration}\:{take}\:{into} \\ $$$${account}\:{the}\:{fact}\:{that}\:{the}\:{force} \\ $$$${F}\left({x}\right)\:{changes}\:{sign}\:{in}\:{interval}. \\ $$

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