To calculate the average velocity, we need to determine the change in position (displacement) and divide it by the time interval.

1. Initial Position: $(x_1, y_1, z_1) = (-2.1, 3.7, 1.4)$
2. Final Position: $(x_2, y_2, z_2) = (3.3, -1.1, -4.2)$
3. Time Interval: $t = 5.3$ seconds

Step 1: Calculate displacement vector

The displacement $\Delta \vec{r}$ is the difference between the final and initial positions:

$\Delta \vec{r} = (x_2 - x_1, y_2 - y_1, z_2 - z_1)$

$\Delta \vec{r} = (3.3 - (-2.1), -1.1 - 3.7, -4.2 - 1.4)$

$\Delta \vec{r} = (5.4, -4.8, -5.6)$

Step 2: Magnitude of displacement

To find the magnitude of the displacement vector:

$|\Delta \vec{r}| = \sqrt{(5.4)^2 + (-4.8)^2 + (-5.6)^2}$

$|\Delta \vec{r}| = \sqrt{29.16 + 23.04 + 31.36} = \sqrt{83.56} \approx 9.14 \, \text{units}$

Step 3: Average velocity

The average velocity is the total displacement divided by the time:

$v_{\text{avg}} = \frac{|\Delta \vec{r}|}{t}$

$v_{\text{avg}} = \frac{9.14}{5.3} \approx 1.72 \, \text{units/second}$

Thus, the average velocity is approximately 1.72 units/second.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the result change if the time interval was shorter?
2. What if the object followed a curved path instead of a straight line?
3. How do you find the direction of the average velocity vector?
4. What is the difference between average speed and average velocity?
5. How would this calculation change in 2D instead of 3D?

Tip: Displacement only considers the initial and final positions, while distance traveled includes the entire path.