Calculating Average Velocity for Displacement Journey

Average velocity is defined as the total displacement divided by the total time taken.

The formula is:

$ \vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t} $

Where:

• $ \vec{v}_{avg} $ is the average velocity
• $ \Delta \vec{x} $ is the total displacement
• $ \Delta t $ is the total time

Determining Total Displacement

We need to consider the direction of movement. Let's assume the eastward direction is positive (+) and the westward direction is negative (-).

• Movement 1: 6 km towards the east = $+6$ km
• Movement 2: 8 km towards the west = $-8$ km

Total Displacement $ \Delta \vec{x} $:

$ \Delta \vec{x} = (+6 \text{ km}) + (-8 \text{ km}) = -2 \text{ km} $

The negative sign indicates the total displacement is towards the west.

Calculating Total Time

The total time is the sum of the time taken for each part of the journey.

• Time 1 = 1 hour
• Time 2 = 1 hour

Total Time $ \Delta t $:

$ \Delta t = 1 \text{ hour} + 1 \text{ hour} = 2 \text{ hours} $

Finding the Average Velocity

Now, we can calculate the average velocity using the total displacement and total time.

$ \vec{v}_{avg} = \frac{-2 \text{ km}}{2 \text{ hours}} = -1 \text{ km/h} $

Since the result is negative, the average velocity is 1 km/h towards the west.