Homework Help: Rolling forces

1. The problem statement, all variables and given/known data
Ball starts to slide with initial speed v0 = 6.5 m/s on horizontal surface. After what time will ball start to roll? Kinetic friction between the ball and the surface is 0.3.
v0 = 6.5 m/s
[tex]\mu[/tex] = 0.3
I = 1/2 mr^2
2. Relevant equations
I have solved this problem but I'm not sure if is correct, so please check....


3. The attempt at a solution

Fk = N [tex]\mu[/tex]
ma = mg[tex]\mu[/tex]
a = g[tex]\mu[/tex]

This is the acceleration which is opposite to direction of the ball so it is slowing it down.
So velocity when it starts to roll must be equal to the "rolling velocity" [tex]\omega[/tex] r (what is correct name in English?)

v(t) = v0 - at = [tex]\omega[/tex] r
[tex]\omega[/tex] = [tex]\frac{v0 - g*mu*t}{r}[/tex]

Ek = Fk*s + (1/2) I[tex]\omega[/tex]^2
When I loose the masses and substitute [tex]\omega[/tex]:

1/2 v0^2 = g*mu*(v/t) + (1/5) * (v0 - g*mu*t)

And that is one equation with one unknown (t).
But equation is pretty big and I suppose I got something wrong...