Define velocity as speed in a given direction

1.2 Motion – Velocity

What is Velocity?

Velocity is the speed in a given direction. It is a vector, meaning it has both magnitude (how fast) and direction (where). Think of a car 🚗 moving east at 60 km/h – the speed is 60 km/h, but the velocity is 60 km/h east.

Speed vs. Velocity

How to Calculate Velocity

1. Find the displacement $\Delta \mathbf{x}$ – the straight‑line change in position.
2. Measure the time interval $t$ taken.
3. Use the formula velocity = displacement ÷ time:

   $\displaystyle \mathbf{v} = \frac{\Delta \mathbf{x}}{t}$

Examples

• A sprinter runs 100 m north in 10 s. $\displaystyle \mathbf{v} = \frac{100\,\text{m}}{10\,\text{s}} = 10\,\text{m s}^{-1}\,\text{north}$
• A cyclist travels 20 km west in 2 h. $\displaystyle \mathbf{v} = \frac{20\,\text{km}}{2\,\text{h}} = 10\,\text{km h}^{-1}\,\text{west}$
• A plane flies 500 km east in 2.5 h. $\displaystyle \mathbf{v} = \frac{500\,\text{km}}{2.5\,\text{h}} = 200\,\text{km h}^{-1}\,\text{east}$

Key Points to Remember

• Velocity is a vector; it tells you how fast and in which direction.
• Speed is the magnitude of velocity and has no direction.
• Use displacement, not distance, when calculating velocity.
• Always include the direction (north, south, east, west, etc.) in velocity.
• Velocity can be positive or negative depending on the chosen coordinate system.