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:

Options

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

Answer

A

Explanation

given that
` a prop (-x) " "rArr " "a=-kx `
`v(dv)/(dx) =-kx rArr (v^(2))/(2) =(kx^(2))/(2) " "rArr" "v^(2)prop x^(2) " "therefore " "loss of K.E. is proportional to `x^(2) `