i'm going to take the time to address a few things you're talking about because i feel you have a very strong intuition (this is obvious) but also a slightly skewed grasp of the physics involved. i'd really like you to take the time to understand the following.
work is not a change in potential energy. work is a change in KINETIC energy. it's kind of a hard concept to grab, however i'll try to explain.
perhaps the easiest to understand form of potential energy is height. in this case, potential energy is defined as
U(h) = mgh
where U is potential energy, m is the mass of the object, g is the acceleration due to gravity (approximated at 9.8 m/s^2), and h is the height of the object RELATIVE to a SPECIFIC point. notice that U is a function of h. one cannot say "what is the potential energy of this book" because it is a function of relative position. one must say, "what is the potential energy of this book in relation to the floor," which is easily calculable. it is entirely possible to change the total energy of a system without doing a significant amount of work. that is to say, one can change the total energy of a system by doing an amount of work that is so minuscule as to be negligible and essentially ignored. this is possible by moving a book up very slowly at a constant speed. now, the only work that was done was the slight change of kinetic energy by applying a vertical force to the book that is slightly greater than its force due to gravity for a very small period of time. something very hard to understand is once the book is moving even the slightest amount, if the velocity remains constant, there is no work being done. this is because the NET force is zero. a net force of anything other than zero requires an acceleration. so, while the book is moving upwards at a constant velocity, the force applied on the book by your hand or whatever is raising it is EXACTLY EQUAL to the force applied on the book by gravity.
so, one changes the height of the book, adding a negligible amount of kinetic energy to the system, and in turn doing a negligible amount of work, all while increasing the mechanical energy. now notice i said mechanical energy. this is a measurement of the TOTAL energy of a system, that is Kinetic and potential. kinetic energy has many forms but the most common and basic equation would be
K(v) = 1/2 m V^2.
K is kinetic energy, m is the mass of the object, and V is the velocity at which the object is moving. again, notice that kinetic energy is a function of VELOCITY. Mechanical energy is DEFINED as the sum of the two, (my three line definition symbol is crude, but it gets the point across)
E = K + U = 1/2mv^2 + mgh
we have to make the distinction between being defined as and being equal to for the simple reason that K is a function of velocity and U is a function of position.
now, i'm gonna go out on a limb here and get a little fancy, but you can skip this next section if you'd like and i'll point out where you should come back. another form of potential energy could be in a spring. if one pulls an object attached to a spring at a constant velocity in the same manner we raised the book, we can change the potential energy of the system while doing negligible work. the Force of the spring is as follows
F = -kx
where k is the spring's constant and x is the position FROM EQUILIBRIUM of the object. Force is the negative derivative of potential energy, that is
F = -dU/dx
which also means
U = -[[integral]] F
this is an easy integral, which yields the following
U(x) = 1/2 k x^2
notice potential energy in this case is a function of x which is the distance relative to the equilibrium.
***continued important stuff***
also notice that the EXTERNAL force of the spring, and the EXTERNAL force of gravity are all opposite the direction of the displacement used for potential energy.
so, we return to the car traveling at a constant velocity of 1m/s. you are entirely correct in saying there is no work being done when the car is moving at a constant velocity of 1m/s. well... almost correct. there is no NET work being done. there is work being done by the car, but there is an equal amount of work being done by friction and air resistance (which of course is like saying i like all apples and granny smiths, because air resistance is a form of friction) in the opposite direction. the largest form amount of frictional work being done at these speeds is going to be the car itself. the engine, the drive train, the wheels, etc, all have an amount of friction, which coupled by the air resistance is going to be equal to the amount of work done in actuality by the combustion of the fuel in the pistons. it's kind of hard to see but consider the following.
if there was no friction besides the friction between the wheels and the ground (ignoring the belt for now) then the car would be accelerating at a constant acceleration of 1m/s^2, which is your figure. this is because the car is exerting a force on the road. if we have a 1000kg car, the force would be 1000 N because F = ma.
if we add in friction the picture changes. assuming the force exerted by the engine is a constant 1000 N the whole way through, we have the following scenario. the air resistance, or should i really just say air friction, the friction of the drive train and all other moving parts in the car all add up to 1000 N. friction by definition is always in the opposite direction of motion. therefore, there is actually a considerable amount of total work being done. the car is doing X amount of Joules over a certain distance, and the friction is doing the same amount of X Joules over the same distance in the opposite direction. therefore, the net work being done is zero (because the net force is zero).
the most recent addition to the confusion is the subject of the rocket car. you're asking where the energy goes. well very simply, it goes into propelling the car forward. a normal car uses the energy to supply a torque to the wheel, which off of the belt supplies a force to the ground. if the friction between the wheels and the road is great enough so the wheels don't slip, the car is propelled forward. however, with the rocket car, things are slightly different. this time, the force of the engine is pushing on the air behind it. now we know newton's little handy dandy law that states for every action there is an equal and opposite reaction. so, the rocket pushes against the air, the air pushes back, and the car is propelled forward.
I think we might be ready to jump on the conveyor belt.
the normal car on the conveyor belt is easy to see. the normal car's engine exerts a torque on the wheels which supply a force to the conveyor belt. the conveyor belt pushes back, and the car is propelled forward relative to the conveyor belt. unfortunately for the car, the belt moves backwards relative to the ground at the same speed the car is moving forwards relative to the conveyor belt. therefore, the car is moving forwards at 1m/s, relative to the belt, the belt is moving back at 1m/s relative to the ground, so the net speed between the car and the ground is 0 m/s.
the rocket car's rocket pushes on the air behind it, which pushes back on the car, propelling the car forward. the conveyor belt however, moves backwards at the same speed the car is moving forwards. here's the difference however. because the car is pushing against the air, the force applied by the conveyor belt onto the wheels only causes the wheels to move at double speed. so, the car moves forward at 1m/s relative to the ground, and the conveyor belt moves backwards at 1m/s relative to the ground. however, the car is moving forwards at 2m/s relative to the conveyor belt, and indeed the wheels are turning as fast. therefore, the rocket car will be propelled forward.
if we look at the plane, we have the same scenario as the rocket car. the plane pushes back on the air, which pushes forward on the plane. the conveyor belt moves back at the same speed, but the wheels rotate at twice the speed, allowing the plane to be propelled forward.
the difference simply is upon what the force is being applied. because the wheels of a car are applying a force to nothing but the conveyor belt, the conveyor belt has an affect on the speed of the wheels which are attached to the car. relativistically speaking, this is essentially the same as driving next to a car on the highway. from the observer in the car, the road is simply a conveyor belt that is moving backwards while the car next to him is trying to move forwards. however, because the road is moving backwards, the car is stationary relative to the observer. in the real conveyor belt, the "observer" could simply be considered the ground.
i hope i've helped. if you have any other questions, please feel free to ask.