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The concept of the work-energy theorem is a fundamental principle of physics that relates the work done on an object to the change in its kinetic energy. This theorem can be expressed as the equation \[ W = \triangle KE\], where \(W\) represents the work done on the object and \(\triangle KE\) represents the change in its kinetic energy.

In the context of our bulldozer example, the work-energy theorem helps us to understand how the force applied by the bulldozer not only moves the dirt from one place to another but also changes its kinetic energy from a state of rest to one of motion. It's essential to note that the total work done also includes overcoming other energy barriers like friction or air resistance, although these aren't explicitly mentioned in the problem.

The term 'force displacement work' refers to the calculation of work done when a force causes an object to move a certain distance. The basic formula for work in the context of force and displacement is \[W = Fd \times \text{cos}\theta\], where \(W\) is the work done, \(F\) is the magnitude of the force applied, \(d\) is the displacement of the object, and \(\theta\) is the angle between the force vector and the direction of displacement.

In our bulldozer scenario, the force is applied in the same direction as the movement of the dirt, which is horizontally for pushing and vertically for lifting. Therefore, the angle \(\theta\) is 0 degrees when pushing and 90 degrees when lifting, leading to \(\cos(0°) = 1\) and \(\cos(90°) = 0\). This simplifies the calculation and allows us to directly multiply the force by the displacement to find the work done for each part of the task.

Mechanical work calculation involves determining the amount of energy transferred by a force to move an object. In our example, there are two separate instances of work: pushing and lifting the dirt. For pushing, the calculation is straightforward as the force and movement are in the same direction. However, for lifting, it's implied that the force is against gravity which would normally involve a consideration of the gravitational field (9.81 m/s^2), but since the force is given, we simply use the vertical displacement.

Summing up the work from both actions provides a complete picture of the energy expenditure by the bulldozer. It did 150,000 Joules of work to push and 4,500 Joules to lift the dirt. This work represents the total energy the bulldozer engine had to produce to achieve both tasks.