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) *x*²

(b) *e*^{x}

(c) *x*

(d) log_{e }x

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Ans: (a)

Sol: $\large -a \propto x $

$\large -v\frac{dv}{dx} = k x$

$\large – \int_{u}^{v} v dv = \int_{0}^{x}k x dx$