1. What Is Velocity?
Velocity tells us how fast an object is moving and in which direction. It is similar to speed, but with one important difference: velocity includes direction.
For example, saying “10 m/s east” is velocity, while “10 m/s” alone is speed.
1.1. Velocity = Speed With Direction
If two objects move at the same speed but in opposite directions, their velocities are different because the directions are different.
1.2. Vector Nature of Velocity
Velocity is a vector quantity. That means it has magnitude (how fast) and direction (which way).
This is why velocity can be positive, negative, or zero depending on the chosen direction.
2. Formula for Velocity
Velocity is calculated using displacement, not distance. The formula is:
\( v = \dfrac{\text{Displacement}}{\text{Time}} \)
This means velocity depends on the shortest straight-line change in position.
2.1. Example of Calculating Velocity
If a person moves 20 meters east in 5 seconds, the velocity is:
\( v = \dfrac{20}{5} = 4 \, \text{m/s east} \)
2.2. Units of Velocity
Velocity is measured in:
- meters per second (m/s)
- kilometers per hour (km/h)
3. Direction and Sign of Velocity
For straight-line motion, we choose one direction as positive and the opposite direction as negative.
3.1. Positive Velocity
If you walk in the chosen positive direction, velocity will be positive.
3.2. Negative Velocity
If you walk in the opposite direction, your velocity becomes negative because displacement becomes negative.
3.3. Zero Velocity
Velocity becomes zero when there is no change in position, even if time passes.
Example: A person standing still has zero velocity.
4. Velocity in Everyday Life
We use the idea of velocity often without realizing it. When someone says “The train is moving north at 60 km/h,” they are talking about velocity.
4.1. Comparing Velocities
Even if two people have the same speed, their velocities differ if they move in different directions.
4.2. Velocity and Motion on Roads
Road signs often display speed, not velocity, because the direction is not fixed. But traffic systems use velocity when analyzing movement patterns.
5. Instantaneous Velocity (Informal Idea)
The velocity of an object at a particular moment is its instantaneous velocity. In simple terms, it is the velocity shown by a speedometer at that instant, along with direction.
5.1. Example
When you're in a moving car, the speedometer shows your speed. If you also note the direction you are moving, that gives you the instantaneous velocity.