With the usual definition of energy, power (rate of energy addition) is equal to force times velocity. The power curve of a rocket is the same as the velocity curve, because the force is constant.

The dotted horizontal line is the amount of power which the engine produces.

At the start, all of the energy goes to the exhaust, because the rocket mass does not have a velocity, and power is proportional to velocity.

There is a point in time when the rocket mass acquires energy at a higher rate than the engine transforms energy. The equation still balances, because the exhaust acquires a negative energy, and the total is still the same as the output of the engine.

But it is impossible for the rocket to acquire more energy than the engine produces. And it is impossible for the exhaust to acquire a negative power.

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