If ω(t) represents the angular speed of the link, then the angular speed at some time "t" is the FUNCTION value of ω(t). On the other hand, the angular acceleration α(t) is the TIME DERIVATIVE of ω(t) ...

For velocity and acceleration, you need derivatives with respect to time. Recall that you can use the chain rule of differentiation in order to effect the derivative of y with respect to time: dy/dt = ...