Velocity

What is Velocity?

✅ Definition:

Velocity is the rate at which an object changes its position in a specific direction.

• It is a vector quantity, meaning it has both:

  • Magnitude (how fast)

  • Direction (where to)

✳️ Example:
A car moving at 60 km/h to the north has a velocity of 60 km/h north.

🔍 Key Characteristics:

🧮 Formula for Velocity:

Velocity=DisplacementTime\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}

• Displacement is the straight-line distance between start and end points (with direction).

• Time is the duration of travel.

🔸 Example:
If a person moves 100 m east in 20 seconds:

Velocity=100 m20 s=5 m/s east\text{Velocity} = \frac{100\text{ m}}{20\text{ s}} = 5\text{ m/s east}

📏 Common Units of Velocity:

🌀 Types of Velocity:

🧠 Real-Life Examples:

• An airplane flying 800 km/h west

• A person walking 1.5 m/s north

• Earth revolving around the Sun (direction constantly changes → changing velocity)

📜 History & Discovery of Velocity Concept

🏛 Ancient Roots:

• The idea of motion was studied by Aristotle (4th century BCE), but he misunderstood velocity, believing heavier objects fall faster.

⚖️ Galileo Galilei (1564–1642):

• Galileo was first to scientifically define velocity.

• He distinguished velocity from acceleration, introducing average velocity.

• He used inclined planes to show that objects accelerate uniformly when falling.

🧪 His experiments laid the foundation of classical mechanics.

🧠 Isaac Newton (1643–1727):

• In 1687, Newton’s Philosophiæ Naturalis Principia Mathematica defined motion with his three laws.

• Newton made velocity a core concept in his Second Law:

  F=m⋅a=m⋅ΔvΔtF = m \cdot a = m \cdot \frac{\Delta v}{\Delta t}

• Newton showed how velocity changes with force over time (acceleration).

🧠 Interesting Facts:

• Velocity can be zero even if speed is not: e.g., running around a track and ending where you started means zero displacement → zero velocity.

• On roller coasters, your speed may stay constant, but direction changes constantly, so velocity changes.

• Light has velocity too: its speed in vacuum is 299,792,458 m/s, but it has a direction → it's a velocity.

📌 Summary Chart: