Velocity is a fundamental concept in physics that describes an object’s motion. It indicates both how fast an object changes position and the specific direction of that change. Understanding velocity helps analyze how objects move in the physical world.
The Common Label for Velocity
In physics and mathematics, velocity is typically represented by the lowercase letter ‘v’. This widely accepted symbol denotes this physical quantity in equations and discussions. Since velocity is a vector quantity, possessing both magnitude and direction, it is often distinguished in written form. This is commonly done by writing ‘v’ in boldface (v) or by placing an arrow above it ($\vec{v}$) to explicitly indicate its vector nature. While ‘v’ is the most frequent symbol, ‘u’ is sometimes used to represent initial velocity, particularly in kinematics equations.
What the Label Represents: Magnitude and Direction
The label ‘v’ encompasses two distinct yet inseparable components: magnitude and direction. The magnitude of velocity refers to how fast an object is moving, which is commonly known as its speed. For instance, a car traveling at 60 kilometers per hour describes its speed. However, for a complete description of its velocity, the direction of motion must also be specified.
The direction indicates the path or orientation along which the object is moving. A car traveling at 60 kilometers per hour north provides a full velocity description, unlike merely stating its speed. If an object’s direction changes, even if its speed remains constant, its velocity is considered to have changed. Both the magnitude and the precise direction are necessary to fully define an object’s velocity.
Units for Expressing Velocity
Velocity is a derived quantity, calculated from an object’s displacement over time. The International System of Units (SI) for velocity is meters per second (m/s). This unit represents the number of meters an object travels in one second.
Beyond the SI unit, other common units are used depending on the context, such as kilometers per hour (km/h) and miles per hour (mph). Vehicle speeds are typically expressed in km/h or mph in everyday usage. All these units fundamentally express a measure of distance covered per unit of time.
Velocity Versus Speed
Velocity and speed are distinct concepts in physics, though often confused. Speed quantifies only how fast an object is moving, making it a scalar quantity with magnitude alone. A car’s speedometer, for instance, displays its speed, indicating only how fast it is traveling at that moment.
In contrast, velocity is a vector quantity, including both magnitude (speed) and specific direction. For example, a car moving at 60 mph is its speed, but 60 mph east describes its velocity. An object traveling in a circular path at a constant speed, like a car on a roundabout, continuously changes direction, meaning its velocity constantly changes even if its speed remains the same.