Q: A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
(a) x²
(b) ex
(c) x
(d) loge x
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Ans: (a)
Sol: $\large -a \propto x $
$\large -v\frac{dv}{dx} = k x$
$\large – \int_{u}^{v} v dv = \int_{0}^{x}k x dx$