A particle is at rest on a rough horizontal plane . The plane is slowly titled until the particle starts to move and is then kept fixed . If the static and kinetic coefficients of friction are `mu_(s)` and `mu_(k) ( lt mu_(s))` respectively , show that the velocity of the particle after it has travelled distance d is given by :
`v = sqrt((2(mu_(s) - mu_(k))"gd")/((1 + mu_(s)^(2))^(1//2)))`