Physics / core

Velocity

Also known as: speed with direction, v

definition

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.

💡 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.

Formal View

Average velocity is defined as \vec{v}_{\text{avg}} = \frac{\Delta \vec{x}}{\Delta t}, and instantaneous velocity is the limit \vec{v} = \lim_{\Delta t \to 0} \frac{\Delta \vec{x}}{\Delta t} = \frac{d\vec{x}}{dt}.

🔬 Example

60 km/h north is a velocity; -10 m/s means moving in the negative direction.

🎯 Why It Matters

Gives a complete description of how an object's position changes over time.

⚠️ Common Confusion

Speed is just the magnitude of velocity; velocity also includes direction.

💭 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.

Related Concepts

Prerequisites

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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Compare With Similar Concepts

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Frequently Asked Questions

What is Velocity in Physics?

The rate of change of position with respect to time, including both magnitude and direction.

Why is Velocity important?

Gives a complete description of how an object's position changes over time.

What do students usually get wrong about Velocity?

Speed is just the magnitude of velocity; velocity also includes direction.

What should I learn before Velocity?

Before studying Velocity, you should understand: displacement.

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