Question

A 0.5kg object is given an initial velocityof 3m/s after when it slides a distance of 8m across a level floor whatis the coefficient of kinetic friction between the object and the floor

Answer 1

You mean it stopped after 8 meters?

If so
average speed = (3+0)/2 = 1.5 m/s

so t = 8/1.5 = 80/15 = 5.33 seconds sliding to a stop

then acceleration a = (0-3)/5.33 = -.5625 m/s^2

so now the physics
F = m a
-m g (mu) = m (-.5625)
mu = .5625/9.81 = .0573