W = Fd, where W is work (in Joules, J), F is the force (in Newtons, N), and d is the distance (in meters, m).

K = (1/2)mv^2, where K is kinetic energy (in Joules, J), m is mass (in kilograms, kg), and v is velocity (in meters per second, m/s).

Ug = mgh, where Ug is gravitational potential energy (in Joules, J), m is mass (in kilograms, kg), g is acceleration due to gravity (9.8 m/s² on Earth), and h is height (in meters, m).

U_{sp} = (1/2)kx^2, where Usp is elastic potential energy (in Joules, J), k is the spring constant (in N/m), and x is the displacement from equilibrium (in meters, m).

P = W/t or P = \Delta K/t, where P is power (in Watts, W), W is work (in Joules, J), \Delta K is the change in kinetic energy (in Joules, J), and t is time (in seconds, s).

A system that allows both matter and energy to be exchanged with its surroundings.

A system that allows energy exchange but not matter exchange with its surroundings.

Work is when a force moves an object over a distance; calculated as $W = Fd$.

The capacity to do work; it comes in many forms (kinetic, potential, thermal, etc.).

The sum of kinetic and potential energy in a system.

Energy of motion; calculated as $K = \frac{1}{2}mv^2$.

Energy due to height above a reference point; calculated as $U_g = mgh$.

Energy stored in a spring or elastic material; calculated as $U_{sp} = \frac{1}{2}kx^2$.

The rate at which work is done or energy is transferred; calculated as $P = \frac{W}{t}$ or $P = \frac{\Delta K}{t}$.

Open System: Allows exchange of both matter and energy with surroundings. | Closed System: Allows exchange of energy but not matter with surroundings.

Kinetic Energy: Energy of motion. | Potential Energy: Energy of position or configuration.

Gravitational Potential Energy: Energy due to height above a reference point. | Elastic Potential Energy: Energy stored in a spring or elastic material.

Work: Transfer of energy by a force acting over a distance. | Power: Rate at which work is done or energy is transferred.