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The force required to compress an imperfect horizontal spring an amount x is given by F = 150x + 12x

I know how to integrate F(x) to get the work done, and with that I could use the work-energy theorem to find the speed. But do I take the lower limit of the integral as x = 2.0 and the upper limit as x = 0?

But then the integral would be negative and 1/2mv

^{3}, where x is in meters and F in Newtons. If the spring is compressed 2.0m, what speed will it give to a 3.0 kg ball held against it and then released?I know how to integrate F(x) to get the work done, and with that I could use the work-energy theorem to find the speed. But do I take the lower limit of the integral as x = 2.0 and the upper limit as x = 0?

But then the integral would be negative and 1/2mv

^{2}can't be negative...
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