Average Velocity

Definition:
Average velocity is defined as the displacement of an object divided by the time taken to cover that displacement. It is a measure of the overall change in position of an object over a given time interval.

Formula:
The formula for average velocity is given by:

v = Δx/Δt

where:
- v is the average velocity
- Δx is the change in position or displacement
- Δt is the change in time

Proof:
To prove that average velocity is equal to the change in position divided by the change in time, we can consider a simple example of a car moving along a straight road.

Example:
Let's say a car travels a distance of 100 kilometers in a time of 2 hours. We can calculate the average velocity of the car using the given formula.

Step 1: Calculate the Change in Position (Δx):
The change in position is simply the final position minus the initial position. In this case, the final position is 100 kilometers and the initial position is 0 kilometers.

Δx = 100 km - 0 km = 100 km

Step 2: Calculate the Change in Time (Δt):
The change in time is the final time minus the initial time. In this case, the final time is 2 hours and the initial time is 0 hours.

Δt = 2 hours - 0 hours = 2 hours

Step 3: Calculate the Average Velocity (v):
Using the formula v = Δx/Δt, we can substitute the values we calculated:

v = 100 km / 2 hours = 50 km/h

Therefore, the average velocity of the car is 50 kilometers per hour.

Conclusion:
The proof above demonstrates that the average velocity is indeed equal to the change in position divided by the change in time. By calculating the displacement and time interval, we can determine the average velocity of an object. Average velocity is an essential concept in physics and is widely used to describe the motion of objects.