Don't think about numbers double quadraple etc.

Think of simple notion. Why more energy is needed to accelerate moving object compared to still?

Kinetic energy possesed by any object is equal to work/effort needed to be made by an external force to accelerate it from present state to stated velocity.

If object is already moving, and i am that external force, first i had to catch up with that object, for that i had to do work make effort until i am moving at same speed as object, even after catching up, at the momennt if i try to push object, i am distracting myself engaging into 2 activity maintaining my speed same as object and trying to push so that will definetely reduce my speed, so i first had to gain slighly more speed than object before i give it a push and transfer all my momentum to object so it accelerates.

Thus i needed more effort or work to do, to accelerate moving object compared to stationary one.

That work done is kinetic energy object posses when it was accelerated from 1 to 2 and its more than when moving object from 0 to 1.

That simply explains the fact. Now how much more energy triple or quadraple that comes down to practical established formulas.

In my understanding OP was confused as when talking about,op was simply thinking if object is already moving it would take less force to move it as it already has gain momentum against all odd of nature and resistive forces, so now only work needed is to accelerate it and it doesn't include loss against resistive forces.

But to accelerate moving object the applier of force whether human or another object also needs to catch up