In physics, work is defined as the product of the force applied on an object and the displacement of that object in the direction of the force. Formula: W = F × d × cos(θ), where θ is the angle between the force and displacement vectors.

The SI unit of work is the Joule (J). One Joule is defined as the work done when a force of one newton displaces an object by one meter in the direction of the force.

The formula for kinetic energy (KE) is KE = (1/2)mv², where m is mass and v is the velocity of the object.

Potential energy is the energy possessed by an object due to its position or configuration. For gravitational potential energy: PE = mgh, where m is mass, g is acceleration due to gravity, and h is height above a reference point.

The work-energy theorem states that the work done by the net force acting on an object is equal to the change in its kinetic energy.

Power is defined as the rate at which work is done or energy is transferred. Formula: Power = Work done / Time taken.

The SI unit of power is the Watt (W). One Watt is equal to one Joule per second.

The scalar product (or dot product) of two vectors A and B is given by A · B = |A||B| cos(θ), where θ is the angle between the vectors. It results in a scalar quantity.

The scalar product follows the commutative property: A · B = B · A.

The distributive property states: A · (B + C) = A · B + A · C.

If two vectors A and B are perpendicular, then A · B = 0.

The work done in lifting an object is calculated using W = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height lifted.

The principle states that energy cannot be created or destroyed, only transformed from one form to another.

Work is the transfer of energy through force applied over a distance, while energy is the capacity to perform work.

Running up the stairs quickly requires more power than walking up because power is the rate of doing work; more work is done in less time.

No, work is only done when an object moves in the direction of the applied force. If there is no displacement, work done is zero.

Work done on an object results in a transfer of energy to that object, changing its kinetic energy or potential energy.