Question

Particle moving in spiral where decreasing radius r is given by \(r=b-ct\) and the angular velocity increases \(w=kt\) . Where b,c,k are constants.
What is the speed as a function of t? What is the speed when r=0?

if tangential velocity is given by \(v=wr\) would that mean the speed is \[s(t)=|wr|=(kt)(b-ct)\]