Average Velocity and Speed

Average Speed

• Definition: Total distance travelled divided by total time taken. $$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$$
• Scalar quantity (no direction)

Average Velocity

• Definition: Total displacement divided by total time taken. $$\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}}$$
• Vector quantity (has direction)

Key Differences

Feature	Average Speed	Average Velocity
Nature	Scalar	Vector
Formula	Total distance / time	Total displacement / time
Sign	Always positive	Can be positive, negative, or zero
Depends on path	Yes	No (only initial and final positions)

Important Points:

• If displacement is zero, average velocity is zero, but average speed can be non-zero.
• Average velocity is not necessarily equal to arithmetic mean of velocities.

Use total displacement and total time, not individual segments, for true average velocity.

Example:

A car travels 60 km at 30 km/h and returns the same distance at 60 km/h. Find:

1. Average speed
2. Average velocity

Solution:

• Total distance = $60 + 60 = 120\ \text{km}$
• Time = $\frac{60}{30} + \frac{60}{60} = 2 + 1 = 3\ \text{h}$
• $$\text{Average Speed} = \frac{120}{3} = 40\ \text{km/h}$$
• $$\text{Displacement} = 0 ⇒ \text{Average Velocity} = 0$$