Is mass relevant on a frictionless surface?

[strategist]

I was looking at a problem: http://gyazo.com/c872ea999197823a42568809f9d97d3f
and I understood that the reason that the force would have to be greater on a surface with friction because the equation for the force of friction is dependent on mass (μk * mg) and with two masses it essentially becomes Mk *2mg.

But the explanation: http://gyazo.com/43b305b3a9159d23ab94fb722a9454d8
got me thinking of what would happen if the surface were frictionless? If I want to push something to a constant speed on a frictionless surface, that would involve a force being applied at a single instant, wouldn't it? Pushing it consistently even with with the same force would continue to accelerate it, I would think. And the reasoning provided by this book implies that the whole reason it would take more force is due to the frictional force applied by the floor on the bottom block.
I can understand that mass is relevant when trying to constantly accelerate a block because F/m = a but does that apply to forces applied only at a single instant in time.

 

[Dr. Courtney]

If there is no friction, then the velocity would be constant in the absence of applied or other forces.

 

[strategist]

If there is no friction, then the velocity would be constant in the absence of applied or other forces.

Oh, I understand that. But what I'm asking is if the mass were greater and the same force were applied, would the velocity be any different?

 

[Dr. Courtney]

Sure. A constant force F applied for a time t, gives an impulse F*t.

The resulting velocity v for a mass m will be v = F*t/m