[المتفيزق]

it is very easy ...
just have the accelleration differentiate s with respect to time twice to have a= 15t -2.6 m/s2
now ma = Fspring-friction
Fspring = -k. s
F friction = -mu. mg
as magnitudes:
Ftotal =k.s + mu.mg
now for the block to slip ma must be greate than F
we take the time when they are just equal ; i.e. Ftotal =ks + mu.mg = m(15t -2.6)
now solve to have t
once having t you can easily compute s from the equation s=2.5t^3-1.3t^2
and that is it .
والله اعلم