η_P=(T*V)/(Q_in ) '

or

overall efficiency = (Thrust * velocity )/ Q'_in

where Q'_in is the rate of thermal energy being release by the burning fuel.

So here is where I'm stuck. Imagine there were two identical rockets in space. And they were both ignited at the same time, the only difference is that rocket A had an initial velocity while rocket B did not.

That equation above (or for that matter, the equation of Power = velocity x force), would state that even though the rockets were burning the same fuel at the same rate, and had the same thrust, rocket A would have a higher power rate, just because its velocity was originally higher. Something about that doesn't seem rate.

Also, with regard to the efficiency equation, couldn't you have an efficiency of over 100%? I mean assume the rocket was traveling through space at 8,000 m/s with the rockets off, and then they were ignited at their lowest setting (assume this setting is so small that it is almost negligible, this make Q_in' very small). So in this case, even though the rocket was barely doing anything, because the initial velocity was so high, the power output would be enormous based on power=force*velocity. And if the initial velocity was high enough (make it any number), the product of thrust*velocity would be much greater than Q'_in, putting the overall efficiency at greater than 100%.

Can anyone clarify this to me, explain to me what I'm not understanding.

Also, how does one import pretty equations into this forum so that you don't have to type out ugly equations?