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A force F=(a+bx) acts on a particle in ...

A force F=(a+bx) acts on a particle in x direction where a and b are constants . Find the work done by this force during displacement from `x_(1)` to `x_(2)` .

Text Solution

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Work done for displacement dx
`dW=Fdx=(a+bx)dx`
Total work done `W= int dW`
`=int_(x_(1))^(x_(2))(a+bx)dx`
`=[ax+(bx^(2))/(2)]_(x_(1))^(x_(2))`
` =a(x_(2)-x_(1))+(b)/(2)(x_(2)^(2) -x_(1)^(2))`
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