W/s is the rate at which power increases. I can't think of an example of where this unit might be commonly used. Claude.
It is the rate at which power is used, as other have said before me. A practical example, you have a power transmission shaft of a car with an applied torque T, with a constant rotational speed, n. You want to determine the power transmitted to the shaft. Then you will have [tex] \dot{W_{sh}} = 2 \pi \dot{n} T [/tex] Edit: Oh, I see you said watts/second. Forget what I said above. That would be the rate of the rate at which power is being used. Well, you could change my n dot to an n double dot, where the n double dot is the rotational acceleration I guess. But I cant see any purpose for doing so. I guess you could interpret it as the rate at which the power being transmitted through the shaft is changing with respect to time, if it has a nonuniform speed, n. If you know n double dot, you can integrate to find the power transmission from [tex] t_0 [/tex] to [tex] t_1 [/tex] [tex] \dot{W_{sh}} = \int^{t_1}_{t_0} \ddot{W_{sh}} dt = \int^{t_1}_{t_0}2 \pi \ddot{n} T dt [/tex]