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A body of mass 8kg is moved by a force F...

A body of mass 8kg is moved by a force F =3x N, where x is the distance covered . Initial position is x= 2m and final position is x = 10m . If initialy the body is at rest , find the final speed .

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`F=ma: F=m.(dv)/(dt)`
`3x=m.(dv)/(dx).(dx)/(dt) , 3x=8.(dv)/(dx)v, 3x dx =8v dv`
`3int_(2)^(10) x dx = 8int_(0)^(v) v dv , 3[(x^(2)/2]_(2)^(10)=8[v^(2)/2]_(0)^(v) ,3[100-4] =8v^(2), v^(2)=(3xx96)/8=36, v=6 m//s`
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