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k = 1/2*m*v

^{2}

This confuses me because this indicates it take more and more energy to accelerate...

Lets imagine a rocket in space (assume the mass of the rocket stays the same when accelerating) - the formula suggests it would take more energy (therefore fuel) to go from 50 to 100 km/s than it would from 0 to 50 km/s.

Is it true that it would take more fuel to accelerate from 50 to 100 km/s than it would from 0 to 50 km/s ?????