Power (Physics)

Definition

Power is the rate at which work is done or energy is transferred. Mathematically, it is the derivative of work with respect to time: $P = \frac{dW}{dt}$ How to read: “P equals d W over d t” Meaning: Instantaneous power is the rate of change of work with respect to time.

For constant work over a time interval $\Delta t$, power is: $P = \frac{W}{\Delta t}$ How to read: “P equals W over delta t” Meaning: Average power is total work done divided by the time interval over which it is done.

Why It Matters

Power determines how quickly a task can be accomplished. In engineering and physics, understanding power is critical for designing engines, motors, and electrical systems that can deliver sufficient energy per unit time to overcome resistance or achieve acceleration.

Core Concepts

• Units: The SI unit of power is the Watt (W), which is 1 Joule per second (J/s).
• Mechanical Power: For a constant force $F$ moving an object at velocity $v$, power is given by: $P = F \cdot v$ How to read: “P equals F dot v” Meaning: Power can be calculated as the dot product of the force vector and the velocity vector.
• Electrical Power: The rate at which electrical energy is converted: $P = I \cdot V$ How to read: “P equals I times V” Meaning: Electrical power is the product of current I and voltage V.
• Efficiency: The ratio of useful power output to total power input.

Connected Concepts

• Work
• Kinetic Energy
• Newton’s Second Law of Motion