newtonian mechanics - How can an object with zero acceleration move?

My physics text has a problem in which it is said that a person moves a block of wood in such a way so that the block moves at a constant velocity. The block, therefore, is in dynamic equilibrium and the vector sum of the forces acting on it is equal to zero:

$\sum{F} = ma = m \times 0 = 0$

This is where I get confused. If the person is moving the block in such a way so that the sum of the forces acting on it is equal to zero, how can he be moving it at all? I realize that

1. even if there is no force acting on an object it can still have velocity (Newton's First Law)


2. force causes acceleration (a change in velocity--not velocity itself)

but for some reason I don't understand how it is possible for the object to move with constant acceleration velocity. Do I have all the pieces? I really feel like I am missing something.

EDIT

The block was at rest to begin with, and the person is moving the block through the air

EDIT: THE ACTUAL PROBLEM

For the sake of clearing up ambiguity, here is the actual problem. (I thought it was wooden blocks at first, sorry)

Two workers must pick up bricks that like on the ground and place them on a worktable. They each pick up the same number of bricks and put them on the same height worktable. They lift the bricks so that the bricks travel upward at a constant velocity. The first gets the job done in one-half the time that the second takes. Did one of the workers do more work than the other? If so, which one? Did one of the workers exert more power than the other? If so, which one?

Basically, the intent of this question is to ask if the above problem is entirely hypothetical. My text does not indicate that it is, which is what I find confusing.

Answer

If the person is moving the block in such a way so that the sum of the forces acting on it is equal to zero, how can he be moving it at all?

Consider a person pushing the block of wood along a surface with friction where the force due to friction (a force proportional to the speed of the block) exactly cancels the pushing force from the person.

The forces add to zero so the block does not accelerate. However, in order for the forces to add to zero, the block must be moving.

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This addendum addresses the (latest) edited version of the question:

The first gets the job done in one-half the time that the second takes. Did one of the workers do more work than the other?

First let's ignore the accelerations at the beginning and end.

Work is force through distance. A brick lifted with constant speed against the pull of gravity to a given height requires a certain amount of work to be done by the worker regardless of the time spent lifting.

So, comparing the amount of work done while the bricks move with constant speed, there is no difference.

However, there is a difference in the power since power is the rate at which work is done.

If the same amount of work is done in half the time, the associated power is double. One worker does work at twice the rate of the other.

Now, let's look at the accelerations. To start a brick moving requires that the worker do work on the brick such that the brick gains kinetic energy.

But to stop the brick moving requires that the brick do work on the worker such that the brick loses that kinetic energy.

Thus, the work associated with the accelerations (ideally) cancel and don't factor into this calculation.

Let's tie this together with your original question:

How can an object with zero acceleration move?

Clearly, in this problem, each brick is at rest, is then briefly accelerated to some speed, moves at this speed for some distance, and then is briefly decelerated to rest.

During the portion in which a brick moves upward with constant speed, the worker provides a force which cancels the force of gravity. The momentum of the brick is constant since there is zero net force acting on the brick.

But, the brick is moving upward due to the brief acceleration where it gained momentum and kinetic energy.