Rockets are usually constant powered, meaning they use fuel at a constant rate. Power is rate of energy addition.

With the usual definition of energy, power is proportional to force times velocity. As velocity varies, the power varies. How can a constant powered rocket have power varying with velocity?

Mathematically, the power of the rocket mass and exhaust mass are added to create the constant power. The velocity of the exhaust decreases at the same rate the velocity of the rocket mass increases, which shows a constant power.

But there is a problem with that analysis. As velocity increases, it reaches a point where the rocket mass has a greater power than the engine produces, which is an impossibility.

For example, a 10 horsepower rocket motor cannot add 1000 horsepower to the rocket mass, and 990 horsepower in the opposite direction to the exhaust mass, to balance equations. A 10 horsepower motor can't do all of that.