Yes, average velocity can indeed be zero. This occurs when an object returns to its starting point, resulting in a net displacement of zero.
Understanding Average Velocity
Average velocity is a fundamental concept in kinematics that describes the rate at which an object changes its position over a period of time. It is a vector quantity, meaning it has both magnitude (speed) and direction.
The formula for average velocity is:
$$ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time Taken}} $$
- Displacement is the shortest distance between the initial and final positions of an object, along with its direction. Unlike distance, which measures the total path traveled, displacement only cares about the start and end points. If an object finishes its journey at the exact same location where it started, its total displacement is zero, regardless of how far it traveled or what path it took.
- Time Taken is the duration over which the motion occurred.
Therefore, if the total displacement is zero, then the average velocity will also be zero.
Average Velocity vs. Average Speed
It's crucial to distinguish average velocity from average speed, as they are often confused but describe different aspects of motion.
- Average Speed: This is a scalar quantity that measures the total distance traveled divided by the total time taken. It only considers the magnitude of motion, not its direction.
$$ \text{Average Speed} = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}} $$
Here’s a concise comparison:
| Feature | Average Velocity | Average Speed |
|---|---|---|
| Type | Vector (magnitude and direction) | Scalar (magnitude only) |
| Formula | Displacement / Time | Total Distance / Time |
| Can be Zero? | Yes, if displacement is zero | No, if the object has moved (distance > 0) |
| Dependent On | Initial and final positions | Entire path taken |
An object can have zero average velocity, but it cannot have zero average speed if it has moved from its initial position. For instance, if an object completes a round trip, its average velocity is zero because its final position is the same as its initial position, leading to zero displacement. However, the object clearly covered a certain distance during its trip, so its average speed would be greater than zero.
Practical Examples of Zero Average Velocity
Consider these everyday scenarios where average velocity would be zero:
-
Round Trip Journey:
- A car drives 50 miles east from town A to town B and then immediately drives 50 miles west back to town A.
- Initial Position: Town A
- Final Position: Town A
- Displacement: 0 miles
- Average Velocity: 0 mph (regardless of the actual time taken)
- Average Speed: Non-zero (since 100 miles were covered)
-
Circular Path:
- A runner completes one full lap around a 400-meter track, finishing exactly where they started.
- Initial Position: Starting line
- Final Position: Starting line
- Displacement: 0 meters
- Average Velocity: 0 m/s
-
Pendulum Swing:
- A pendulum swings from its highest point on one side to its highest point on the other side, and then back to its original highest point.
- Initial Position: Highest point A
- Final Position: Highest point A
- Displacement: 0
- Average Velocity: 0
In all these examples, while the objects were clearly in motion and covered a certain distance, their net change in position was zero, leading to an average velocity of zero.
