The average velocity in physics is calculated as the displacement divided by the time interval over which that displacement occurred.
Here's a breakdown:
1. Understanding the Key Terms
- Displacement: The change in position of an object. It's a vector quantity, meaning it has both magnitude and direction. Think of it as the straight-line distance between the starting and ending points.
- Time Interval: The duration over which the displacement occurred.
- Velocity: The rate at which an object changes its position. It is a vector quantity.
- Average Velocity: The total displacement divided by the total time. It represents the constant velocity required to achieve the same displacement in the same time interval.
2. The Formula
The average velocity ((\bar{v})) is calculated using the following formula:
(\bar{v} = \frac{\Delta x}{\Delta t})
Where:
- (\Delta x) is the displacement (final position - initial position)
- (\Delta t) is the time interval (final time - initial time)
3. Step-by-Step Calculation
- Determine the Displacement ((\Delta x)): Subtract the initial position from the final position. Remember to include the direction (e.g., + for right, - for left).
- Determine the Time Interval ((\Delta t)): Subtract the initial time from the final time.
- Divide the Displacement by the Time Interval: (\bar{v} = \frac{\Delta x}{\Delta t})
- Include Units: Velocity is typically expressed in meters per second (m/s) or kilometers per hour (km/h). Don't forget to include the appropriate units in your answer.
4. Example
Let's say a car travels from position (x_i = 10) meters to position (x_f = 50) meters in a time interval from (t_i = 2) seconds to (t_f = 6) seconds.
- Displacement: (\Delta x = x_f - x_i = 50 \text{ m} - 10 \text{ m} = 40 \text{ m})
- Time Interval: (\Delta t = t_f - t_i = 6 \text{ s} - 2 \text{ s} = 4 \text{ s})
- Average Velocity: (\bar{v} = \frac{40 \text{ m}}{4 \text{ s}} = 10 \text{ m/s})
Therefore, the average velocity of the car is 10 m/s.
5. Alternative Formula (Constant Acceleration)
If the acceleration is constant, you can also calculate average velocity using:
(\bar{v} = \frac{v_i + v_f}{2})
Where:
- (v_i) is the initial velocity
- (v_f) is the final velocity
Important Note: This formula only works if the acceleration is constant. If the acceleration is not constant, you must use the displacement/time formula.
In summary, calculating average velocity involves determining the displacement and the time interval, then dividing the displacement by the time. Ensure you're using the correct formula based on whether the acceleration is constant or not.
