Velocity question Watch

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Splinter
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Report Thread starter 13 years ago
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Could someone please help me on this, I dont even know how to start, it just confused me.

The Equation of motion of a particle with mass m, subjected to a force kx can be written as kx = mv(dv/dx), where x is the displacement and v is the velocity. When x = 0, v = v(0)
Find v in terms of v(0), k and m, when x = 2
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(Original post by Splinter)
Could someone please help me on this, I dont even know how to start, it just confused me.

The Equation of motion of a particle with mass m, subjected to a force kx can be written as kx = mv(dv/dx), where x is the displacement and v is the velocity. When x = 0, v = v(0)
Find v in terms of v(0), k and m, when x = 2
kx = mv(dv/dx)
dv/dx = kx/mv
mv dv/dx = kx
integrate w.r.t.x
integral mv.dv = integral kx.dx
mv^2 / 2 = kx^2 / 2 + c
mv^2 = kx^2 + C = > v = sqrt [(kx^2 + c)/m]
when x=0, v=v(o) => c=mv(0)^2
When x=2, v = sqrt [(4k + mv(0)^2)/m]
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Splinter
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Report Thread starter 13 years ago
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tahnk you very much. I just didnt get what i was supposed to be doing, as soon as I saw your 3rd line it all made sense. Thx again
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