The state of constant motion along a straight path or being at rest defines a state of the system known as inertia. Force is some agency that disturbs the state of inertia. Force causes acceleration (precisely, a change in momentum). Newton's second law of motion states that
$$\vec{F}=\frac{d\vec{p}}{dt}$$
If the body is moving at a constant velocity, then there is no change in momentum and so
$$\frac{d\vec{p}}{dt}=0\implies\vec{F}=0$$
Hence constant motion means no external unbalanced force is acting on the body. Since there is no force, there is no work done (Since $W=\int\vec{F}\cdot d\vec{s}$).
Hence no work is necessary to be done on a body to maintain it at a constant speed, because no force is required for a body to move with constant velocity. There is displacement of course. The fact is that the displacement that happens here during a constant motion here is not the consequence of the force. The displacement term appearing in the equation of work:
$$\text{Work done}= \text{Force} \times \text{displacement along the direction of applied force}$$
is the displacement as a consequence of the applied force. The dot product between force and displacement (picks up the component of displacement in the direction of the force) vanishes if the force and displacement are independent of each other (or orthogonal to each other in some sense). Here the displacement happens not due to any force. So, the component of force that caused the displacement is zero. Hence there is no work done.
Then by the work energy theorem, there is no change in the kinetic energy of the body. Hence the conservation of energy. This makes sense. No work is done on the body as there is no force to do that. The body is under constant motion, which means momentum is conserved. That is, $p=\text{constant}\implies \Delta p=0$ and so $K.E=p^2/2m=\text{constant}\implies\Delta K.E=(\Delta p)^2/2m=0$.
Conclusions:
- An unbalanced force causes acceleration. It cannot make objects move at constant velocity. Constant velocity is achieved only in the absence of an external force.
- According to Newton's second law, a force is not necessary to keep an object in motion (there is motion, a constant one, possible even in the absence of a force). However the motion will be an unaccelerated one, and takes place along a straight line.
- So, in constant motion, the displacement is not due to some force. The force is absent and so the work done is zero.
- Since the object is moving at a constant velocity, its momentum is not changing, which means that the kinetic energy of the body is not changing. So work done is zero implies the change in kinetic energy is zero. Hence the work- energy theorem.
$W=\Delta K_\text{system}$ and $W_\text{external}=\Delta K_\text{system}+\Delta V$ are consistent with each other iff $\Delta V=-W_\text{internal}$. The latter is the definition of the potential energy for conservative forces.
The cited equation is thus valid iff all internal forces are conservative.
Best Answer
The total work can be split up into two parts:
$$W_{net} = W_{conservative}+W_{non-conservative}.$$
With the conservative part you can associate a potential energy:
$$W_{conservative}=-\Delta PE$$
(this is in fact the definition of a conservative force) so that the Work-Energy theorem becomes
$$W_{non-conservative}=\Delta KE + \Delta PE = \Delta E.$$
This is another way of writing the Work-Energy theorem and in my mind it's a little bit clearer. Restated, the work done by non-conservative forces is equal to the overall change in energy of the system.
For example, work done by friction is negative, so it dissipates energy away from a system.
On the other hand, gravity is a conservative force. Imagine the motion of a falling ball. Unless something doing work on the ball to slow it down (for example, air) the ball will speed up as it falls. In this case, the equation
$$W_{gravity} = -\Delta PE = \Delta KE$$
is equivalent to that statement. (As the potential energy becomes more negative, kinetic energy becomes more positive.)