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

Quantity	Symbol	Unit	Direction	Example
Speed	\$v\$	m s^-1	None (scalar)	10 m s^-1
Velocity	\$\mathbf{v}\$	m s^-1	Yes (vector)	10 m s^-1 north

How to Calculate Velocity

Find the displacement \$\Delta \mathbf{x}\$ – the straight‑line change in position.

Measure the time interval \$t\$ taken.

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.