Explanation:
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Answer:
The work done by a particle from x = 0 to x = 2 m is 20 J.
Explanation:
A force on a particle depends on position constrained to move along the x-axis, is given by,
![F(x)=(3\ N/m^2)x^2+(6\ N/m)x](https://tex.z-dn.net/?f=F%28x%29%3D%283%5C%20N%2Fm%5E2%29x%5E2%2B%286%5C%20N%2Fm%29x)
We need to find the work done on a particle that moves from x = 0.00 m to x = 2.00 m.
We know that the work done by a particle is given by the formula as follows :
![W=\int\limits {F{\cdot} dx}](https://tex.z-dn.net/?f=W%3D%5Cint%5Climits%20%7BF%7B%5Ccdot%7D%20dx%7D)
![W=\int\limits^2_0 {(3x^2+6x){\cdot} dx} \\\\W={(x^3}+3x^2)_0^2\\\\\W={(2^3}+3(2)^2)\\\\W=20\ J](https://tex.z-dn.net/?f=W%3D%5Cint%5Climits%5E2_0%20%7B%283x%5E2%2B6x%29%7B%5Ccdot%7D%20dx%7D%20%5C%5C%5C%5CW%3D%7B%28x%5E3%7D%2B3x%5E2%29_0%5E2%5C%5C%5C%5C%5CW%3D%7B%282%5E3%7D%2B3%282%29%5E2%29%5C%5C%5C%5CW%3D20%5C%20J)
So, the work done by a particle from x = 0 to x = 2 m is 20 J. Hence, this is the required solution.
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