A child slides a block of mass 2 kg along a slick kitchen floor. If the initial speed is 4m/s and the block hits a spring with spring constant 6 N/m, what is the maximum compression of the spring? What is the result if the block slides across 2m of a rough floor that ha μk = 0.2? (second part of the problem) getting to the spring.. vf2=v02+2as F(friction)=μ(mg) ------------> a=μg vf2=v02+2(μg)s vf2= 8.152m/s at the spring.. vf2=v02+2as vf2=0 v02=8.152 [itex]\Sigma[/itex]F=F(friction)+F(spring)=-m|μg|-|kx| a=-|μg|-(|kx|/m) v02=2(-|μg|-(|kx|/m))s but when i plug all the numbers in.. i get a quadratic equation and it ends up having an imaginary component because the "b^2" term, within the quadratic formula ends up being less than the "4ac" term. i COULD go through and just solve it.. but i don't know what to do because i don't know what to do with the imaginaries.