A bolck of mass `10 kg` is moving in x-direction with a constant speed of `10 m//s`. it is subjected to a retardeng force `F=-0.1 x J//m`. During its travel from `x =20m` to `x =30 m`. Its final kinetic energy will be .

Options

A. `475 J`
B. `450 J`
C. `275 J`
D. `250 J`

Answer

A

Explanation

Using work -energy therom , `W_("total") = Delta K`
`W = (1)/(2) m(upsilon^(2) - u^(2))`
`implies (1)/(2) m upsilon^(2) = W+ (1)/(2) mu^(2)`
`Wunderset(20)overset(30)intF.dx=underset(20)overset(30)int0.1.x.dx`
`= - 0.1 int_(20)^(30) xx dx + (1)/(2) xx 10 xx 10^(2)`
` = - 25J + 500J = 475 J`