The rate of change of position with respect to time, including both magnitude and direction. Gives a complete description of how an object's position changes over time.
Definition
The rate of change of position with respect to time, including both magnitude and direction.
💡 Intuition
How fast something is moving AND which way it's heading—direction is essential.
🎯 Core Idea
Velocity is a vector quantity—it has both magnitude (speed) and a direction.
Example
Formula
Notation
\vec{v} is the velocity vector in m/s, \Delta \vec{x} is the displacement vector in metres, \Delta t is the time interval in seconds, and d\vec{x}/dt denotes the derivative of position with respect to time.
🌟 Why It Matters
Gives a complete description of how an object's position changes over time.
💭 Hint When Stuck
When solving a velocity problem, first identify the displacement (change in position) and the time interval. Then divide displacement by time: v = \Delta x / \Delta t. Finally, include the direction in your answer — velocity is a vector, so '5 m/s north' is a complete answer while '5 m/s' alone is just speed.
Formal View
Related Concepts
Compare With Similar Concepts
🚧 Common Stuck Point
Speed is just the magnitude of velocity; velocity also includes direction.
⚠️ Common Mistakes
- Using total distance instead of displacement — a round trip of 10 km out and back has zero average velocity but 20 km of distance.
- Dropping the direction and treating velocity as if it were speed — velocity is a vector quantity.
- Confusing instantaneous velocity with average velocity — average velocity uses total displacement over total time, while instantaneous is the velocity at one specific moment.
Go Deeper
Frequently Asked Questions
What is Velocity in Physics?
The rate of change of position with respect to time, including both magnitude and direction.
What is the Velocity formula?
When do you use Velocity?
When solving a velocity problem, first identify the displacement (change in position) and the time interval. Then divide displacement by time: v = \Delta x / \Delta t. Finally, include the direction in your answer — velocity is a vector, so '5 m/s north' is a complete answer while '5 m/s' alone is just speed.
Prerequisites
Next Steps
Cross-Subject Connections
How Velocity Connects to Other Ideas
To understand velocity, you should first be comfortable with displacement. Once you have a solid grasp of velocity, you can move on to acceleration and speed.
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