A particle moves in a straight line with retardation proportional to its displacement. Its loss in kinetic energy for any displacement x is proportional to

Options

A. `log_(e)x`
B. `x`
C. `e^(x)`
D. `x^(2)`

Answer

D

Explanation

`F prop (1)/(V) " " therefore F=(C )/(v)`
where C is a constant.
`therefore m xx a = (C )/(v) " " therefore m(dv)/(dt)=(C )/(v)`
`therefore vdv = (C )/(m)dt`
Integrating both sides, we get, `therefore (v^(2))/(2)=(Ct)/(m)`
`therefore K.E. = (1)/(2)mv^(2)=(Ct)/(m)xx m=Ct`
`therefore K.E. prop t`