(iv) Find the average velocity over the time interval $$ [4,4.5] $$. Average Velocity $$ =1.4 $$ (D) meters per second.

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To find the **average velocity** over a specific time interval, you'll need to know the **position function** of the object, typically denoted as $$ s(t) $$, where $$ t $$ is time. The average velocity ($$ \overline{v} $$) over the interval $$[t_1, t_2]$$ is calculated using the following formula:

$$
\overline{v} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}
$$

**Given:**
- Time interval: $$[4, 4.5]$$ seconds
- Average Velocity ($$ \overline{v} $$) is claimed to be $$1.4$$ meters per second (m/s)

**Steps to Calculate Average Velocity:**

1. **Determine the Position at $$ t = 4 $$ and $$ t = 4.5 $$:**
   - $$ s(4) $$: Position at $$ t = 4 $$ seconds
   - $$ s(4.5) $$: Position at $$ t = 4.5 $$ seconds

2. **Apply the Average Velocity Formula:**
   $$
   \overline{v} = \frac{s(4.5) - s(4)}{4.5 - 4} = \frac{s(4.5) - s(4)}{0.5}
   $$

3. **Calculate the Difference in Position and Divide by the Time Interval:**
   - Subtract the position at $$ t = 4 $$ seconds from the position at $$ t = 4.5 $$ seconds.
   - Divide the result by $$ 0.5 $$ seconds to find the average velocity.

**Example Calculation:**

Let's assume you have the following position data:
- $$ s(4) = 10 $$ meters
- $$ s(4.5) = 11.4 $$ meters

Then,
$$
\overline{v} = \frac{11.4\, \text{m} - 10\, \text{m}}{0.5\, \text{s}} = \frac{1.4\, \text{m}}{0.5\, \text{s}} = 2.8\, \text{m/s}
$$

**Clarification on Your Answer:**

You mentioned that the average velocity is $$1.4$$ meters per second. Based on the formula:

$$
\overline{v} = \frac{s(4.5) - s(4)}{0.5}
$$

If $$ s(4.5) - s(4) = 0.7 $$ meters, then:

$$
\overline{v} = \frac{0.7\, \text{m}}{0.5\, \text{s}} = 1.4\, \text{m/s}
$$

So, if the change in position ($$ s(4.5) - s(4) $$) is indeed $$0.7$$ meters over the $$0.5$$ second interval, then your calculation of an average velocity of $$1.4$$ m/s is **correct**.

**Final Answer:**

The average velocity over the time interval $$[4, 4.5]$$ seconds is **1.4 meters per second (D)**, assuming that the change in position during this interval is $$0.7$$ meters.
The average velocity over the time interval $$[4, 4.5]$$ seconds is **1.4 meters per second (D)**.

(iv) Find the average velocity over the time interval \( [4,4.5] \). Average Velocity \( =1.4 \) (D) meters per second.

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