Average velocity equals distance travelled divided by speed time
The Correct Answer and Explanation is:
Correct Answer:
Average velocity = Total displacement ÷ Total time taken
Explanation
There is a common confusion between average velocity and average speed, but they are distinct concepts in physics. The formula stated in your question—“average velocity equals distance travelled divided by speed time”—is incorrect. Let’s clarify this.
1. Definitions:
- Average Velocity is a vector quantity. It considers the direction and is defined as: Average Velocity=Total DisplacementTotal Time Taken\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time Taken}}Average Velocity=Total Time TakenTotal Displacement Displacement is the change in position from the starting point to the final point, regardless of the path taken.
- Average Speed, on the other hand, is a scalar quantity. It only considers the magnitude (how much ground is covered), and is calculated as: Average Speed=Total Distance TravelledTotal Time Taken\text{Average Speed} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}}Average Speed=Total Time TakenTotal Distance Travelled
2. Common Mistake:
The incorrect expression you mentioned, “distance travelled divided by speed time,” doesn’t make physical sense. If we break it down:
- “Speed time” would mean multiplying speed and time, which gives distance.
- So, “distance ÷ (speed × time)” = distance ÷ distance = 1 (dimensionless), which doesn’t yield velocity.
3. Example to Understand Better:
Imagine a car moves 100 meters east in 10 seconds and then 100 meters west in another 10 seconds:
- Total distance travelled = 200 meters.
- Total displacement = 0 meters (since it ends up where it started).
- Average speed = 200 m ÷ 20 s = 10 m/s.
- Average velocity = 0 m ÷ 20 s = 0 m/s (because the displacement is zero).
This shows how average velocity can be zero even if movement occurred—because it depends on displacement, not total path covered.
In conclusion, always use displacement (not distance) and total time when calculating average velocity.
