Question

A particle moves along the x axis from x=0 to x=5m under an influence of a force given by f=7-2x+3x square.Find the work done in the process

Answer 1

Work done = F.S = 18X5 = 90

Answer 2

Explanation:

$\Large{\underline{\sf{\blue{Given:}}}}$

$\sf{A\:particle\:moves\:from\:x\:=\:0\:\:to\:\:x\:=\:5m}$

$\sf{F\:=\:7-2x+3x^2}$

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$\Large{\underline{\sf{\red{To\:Find:}}}}$

- $\sf{Work\:done\:in\:the\:process}$

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$\Large{\underline{\sf{\green{Solution:}}}}$

$\sf F\:=\:7\,-2x\,+3x^2$

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$\sf{W\:=\:}$ $\displaystyle\int\limits_{x=0}^{x=5} fdx$

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$\sf{W\:=\:}$ $\displaystyle\int\limits_{0}^{5} 7\,-2x\,+3x^2 dx$

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$\sf{W}$ $\sf \:=\: \left[7x \dfrac{2x^2}{2}+ \dfrac{3x^3}{3}\right]_{0}^{5}$

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$\sf{W}$ $\sf \:=\: \left[7x-x^2+x^3\right]_{0}^{5}$

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$\sf \therefore W$ $\sf \:=\: \left[7\times 5-(5)^2+(5)^3-0\right]$

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$\sf{\implies W\:=\:(35\:-25\:+25)J}$

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$\boxed{\Large{\sf{\pink{Work\:done\:=\:135\,J}}}}$