I was trying to do some first order circuits and there was this one that kind of confused me. Correct me if I'm wrong but if $$V_s=u(t)V$$ this means that for t<0 Vs=0 and for t>0 Vs=1 right?

So therefore my question. For t<0 since technically there is no voltage generator does that mean that the current ix=0 and therefore the dependent source 2ix=0? So in total there is no current whatsoever in the circuit? which means the capacitor is not charged initially?

I am not searching for someone to solve this. I'm just asking for some direction.