A block of mass 10 kg, moving in x-direction with a constant speed of `10ms^(-1)`, is subjected to a retarding force `F=0.1xxJ//m` during its travel from x=20 m to 30 m. Its final KE will be

Options

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

Answer

D

Explanation

`a = (0.1x)/(10) = 0.01 x = V (dV)/(dx)`
So , `int_(v_1)^(V^2)VdV = int_(20)^(30)x/100 dx `
`|V^2/2|^2 =|x^2/200|_(20)^(30)=(30xx30)/200 - (20 xx20)/200= 4.5 -2 =2.5`
`1/2 mv_2^2 =1/2 mv_1^2 -25 =1/2 xx 10 xx 10 xx10 -25`
`=500 - 25 J = 475 J`