A particle moves in a straight line with constant speed of `4 m//s` for `2 s,` then with `6 m//s` for `3 s.` Find the average speed of the particle in the given time interval.

Explanation

To find the average speed of the particle over the given time interval, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Speed during the first interval (v1) = 4 m/s
- Time for the first interval (t1) = 2 s
- Speed during the second interval (v2) = 6 m/s
- Time for the second interval (t2) = 3 s

2. **Calculate the Distance for Each Interval:**
- Distance during the first interval (d1) can be calculated using the formula:
\[ d1 = v1 \times t1 = 4 \, \text{m/s} \times 2 \, \text{s} = 8 \, \text{m} \]
- Distance during the second interval (d2) can be calculated similarly:
\[ d2 = v2 \times t2 = 6 \, \text{m/s} \times 3 \, \text{s} = 18 \, \text{m} \]

3. **Calculate the Total Distance:**
- Total distance (D) is the sum of d1 and d2:
\[ D = d1 + d2 = 8 \, \text{m} + 18 \, \text{m} = 26 \, \text{m} \]

4. **Calculate the Total Time:**
- Total time (T) is the sum of t1 and t2:
\[ T = t1 + t2 = 2 \, \text{s} + 3 \, \text{s} = 5 \, \text{s} \]

5. **Calculate the Average Speed:**
- Average speed (V_avg) can be calculated using the formula:
\[ V_{avg} = \frac{D}{T} = \frac{26 \, \text{m}}{5 \, \text{s}} = 5.2 \, \text{m/s} \]

### Final Answer:
The average speed of the particle in the given time interval is **5.2 m/s**.

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