Work

Work is a fundamental concept in physics dealing with energy transfer.
Defined as the product of the force applied to an object and the distance moved by the object in the direction of the force. Expressed mathematically as Work (W) = Force (F) * Distance (d).
It has the unit of Joules (J) in the International System of Units (SI). It’s important to remember that 1 Joule equals 1 Newton metre (Nm).
Work is considered to be done on an object when the force applied causes displacement of the object.
It is considered positive when force and displacement are in the same direction; conversely, work is considered negative when force and displacement are in opposite directions.
Work is a scalar quantity, as it has magnitude but no direction. If an object moves in a circular path, the total work done is zero, because the force and displacement are perpendicular to each other.
Kinetic energy of an object increases when work is done on the object, and it decreases when work is done by the object. This is the basis of the work-energy theorem.

Principle of Work and Energy

The total work done on a particle is equal to the change in its kinetic energy.
Takes into account not only the work done by the external forces but also by the internal forces.
Useful in solving problems involving work and energy, for example, finding the work done for an object to reach a certain velocity or the velocity of an object after a certain amount of work is done on it.

Work done by Variable Forces

If the force acting on an object is not constant, we integrate to find the work done.
The principle of integration can also be used when the force depends on the position of the objects in their path of motion.
Integration allows for the calculation of work done by varying forces across distances.

Conservation of Mechanical Energy

The total mechanical energy (potential energy plus kinetic energy) of an isolated system, subject to conservative forces, remains constant.
Conservation of energy plays a critical role in work and energy problems.

Power

Power is the rate at which work is done, which is the amount of work per unit time.
Power has the unit Watts (W) in the International System of Units (SI), i.e., 1 Watt equals 1 Joule per second (J/s).
Power is also considered when discussing the efficiency or efficacy of work done by a system or machine.

Remember, a sound understanding of these concepts is essential to effectively answer questions on work, energy and power. These should be combined with rigorous practice for thorough preparation.