To find the average velocity, we use the formula:

$\text{Average Velocity} = \frac{\Delta x}{\Delta t}$

Where:

• $\Delta x = x_2 - x_1$ is the change in position.
• $\Delta t = t_2 - t_1$ is the change in time.

Given:

• $x_1 = 6.2 \, \text{cm}$
• $x_2 = 9.5 \, \text{cm}$
• $t_1 = -4.0 \, \text{s}$
• $t_2 = 3.4 \, \text{s}$

Now, let's calculate the changes:

$\Delta x = 9.5 \, \text{cm} - 6.2 \, \text{cm} = 3.3 \, \text{cm}$

$\Delta t = 3.4 \, \text{s} - (-4.0 \, \text{s}) = 3.4 \, \text{s} + 4.0 \, \text{s} = 7.4 \, \text{s}$

So, the average velocity is:

$\text{Average Velocity} = \frac{3.3 \, \text{cm}}{7.4 \, \text{s}} \approx 0.446 \, \text{cm/s}$

The average velocity of the particle is approximately $0.446 \, \text{cm/s}$.

Would you like more details on this? Here are five related questions to consider:

1. How does average velocity differ from instantaneous velocity?
2. Can the average velocity be zero even if the particle has moved?
3. What is the significance of the sign of the average velocity?
4. How would the calculation change if the position was given in meters instead of centimeters?
5. How does average speed differ from average velocity?

Tip: Remember that velocity is a vector quantity, meaning it has both magnitude and direction.