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  4. A particle is moving under the influence of a force given by F=kx, where k is a constant and x is the distance moved. The energy (in joules) gained by the particle in moving from x=0 to x=3 is

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Q. A particle is moving under the influence of a force given by $ F=kx, $ where $ k $ is a constant and $ x $ is the distance moved. The energy (in joules) gained by the particle in moving from $ x=0 $ to $ x=3 $ is

KEAMKEAM 2008Work, Energy and Power

Solution:

$ U=\frac{1}{2}k(x_{2}^{2}-x_{1}^{2}) $
$ =\frac{1}{2}k({{3}^{2}}-{{0}^{2}}) $
$ =\frac{9}{2}k=4.5\,k $