Speed tells you how fast something is going (a scalar quantity), while velocity tells you how fast and in what direction (a vector quantity).

What are Speed and Velocity?

Both speed and velocity tell us how fast an object is moving, but velocity adds a crucial piece of information: direction.

Speed

Speed is the rate at which an object covers distance. It tells you how fast you’re going, regardless of the direction.

  • Key Idea: “How fast is it going?”
  • Nature: Speed is a scalar quantity. It only has magnitude (e.g., 50 km/h, 30 m/s).
  • Formula: Average speed is calculated as total distance divided by total time: \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
  • Units: Meters per second (m/s) in the SI system, but also km/h, mph, etc.

Velocity

Velocity is the rate at which an object changes its position in a specific direction. It tells you how fast you’re going and in what direction.

  • Key Idea: “How fast is it going, and in what direction?”
  • Nature: Velocity is a vector quantity. It has both magnitude (speed) and direction (e.g., 50 km/h North, 30 m/s downwards).
  • Formula: Average velocity is calculated as displacement divided by total time: \(\text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} = \frac{\Delta x}{\Delta t}\) Remember, $\Delta x$ is displacement, which includes direction.
  • Units: Meters per second (m/s) in the SI system, always with a specified direction.

Interactive Circular Motion

Observe how an object moving in a circle maintains a constant speed but has a constantly changing velocity.

Uniform Circular Motion Simulator A simulation showing an object in uniform circular motion, displaying its velocity and centripetal acceleration vectors. Center V a_c Speed: 0.0 m/s Acc: 0.0 m/s²

Adjust speed and radius, then click "Play" to see uniform circular motion!

Why This Matters?

The distinction between speed and velocity is vital in physics because:

  • It allows for a complete and unambiguous description of motion.
  • It’s essential for understanding acceleration, which is the rate of change of velocity, not just speed.
  • It’s critical for predicting future positions and interactions in multi-dimensional motion.

Interactive Match: Speed and Velocity

Test your understanding of key terms related to speed and velocity by matching them with their meanings.

Click a term and then its matching meaning. Match all pairs to complete!

💡 Quick Concept Check:

A car's speedometer reads 60 km/h. Is this measuring the car's speed or its velocity?

Click to Reveal Answer
The speedometer measures the car's speed. It tells you how fast you are going (magnitude) but not the direction.

Suggested Visuals & Animations:

To make this concept truly “unstuck” and visual:

  1. Circular Track Animation: An object moving around a circular track at a constant speed. Show its speed value remaining constant, but its velocity vector (an arrow) constantly changing direction.
  2. Number Line Motion with Direction: An animated dot moving on a number line. When it moves right, show positive velocity. When it moves left, show negative velocity. Always show speed as the absolute value of velocity.
  3. GPS vs. Speedometer: A visual comparing a car’s speedometer (speed) to a GPS display that shows both current speed and direction of travel (velocity).
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