Answer this.

Object 1, M=1, V=4, Ke=8, P=4
Object 2, M=2, V=2, Ke=4, P=4
Object 3, M=4, V=1, Ke=2, P=4
Object 4, M=1, V=2, Ke=2, P=2
Object 5, M=0.125, V=4, Ke=2, P=0.5

Why does it take more energy to give a mass the same momentum as a larger mass?

Object1, M=1
V=1, P=1, Ke=0.5
V=2, P=2, Ke=2
V=3, P=3, Ke=4.5

When an object is accelerating without resistance, why does it take more and more energy to accelerate it the same amount?

momentum is just product of mass and velocity, so for a constant mass to get more momentum, it requires greater velocity.  It takes energy to accelerate a mass to that greater velocity.  A small mass would need more velocity than a large mass for their momentums to be equal, as in 2x6 = 3x4, where a 2 needs a 6 multiplied to become 12, but the 3 only needs a 4 mulitplied to be 12.

#2 You can't sustain acceleration without energy transfer.  F=ma, to accelerate a mass, you require a force to be applied, and the application of force that has effect over a distance is energy transfer.  When you stop applying the force, you aren't feeding the acceleration anymore.