Define velocity as speed in a given direction

Cambridge IGCSE Physics 0625 – Motion

Objective: Define velocity as speed in a given direction

In physics, velocity is a vector quantity that describes how fast an object moves and the direction of its motion. It can be expressed as:

\$\mathbf{v} = \frac{\Delta \mathbf{s}}{\Delta t}\$

where \$\Delta \mathbf{s}\$ is the displacement (change in position) and \$\Delta t\$ is the elapsed time. Because displacement includes direction, velocity always has a direction associated with it.

Key Differences Between Speed and \cdot elocity

• Nature: Speed is a scalar (magnitude only); velocity is a vector (magnitude + direction).
• Symbol: Speed is usually denoted by \$s\$ or \$v\$ (without an arrow); velocity is denoted by \$\mathbf{v}\$ or \$v\$ with a direction indicator.
• Units: Both are measured in metres per second (m s⁻¹) in the SI system, but velocity’s unit is understood to include a direction.
• Calculation: Speed = total distance travelled ÷ time; velocity = displacement ÷ time.

How to Calculate Average \cdot elocity

1. Identify the initial and final positions of the object.
2. Determine the straight‑line displacement \$\Delta \mathbf{s}\$ (including direction).
3. Measure the time interval \$\Delta t\$ over which the displacement occurs.
4. Apply the formula \$\mathbf{v} = \dfrac{\Delta \mathbf{s}}{\Delta t}\$.
5. State the result with both magnitude and direction (e.g., \$5\ \text{m s}^{-1}\$ east).

Comparison Table