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, we can follow these steps:

### Step 1: Calculate the distance traveled during the first segment of motion.
The particle moves with a constant speed of 4 m/s for 2 seconds.
- Distance \( s_1 = \text{speed} \times \text{time} = 4 \, \text{m/s} \times 2 \, \text{s} = 8 \, \text{m} \)

### Step 2: Calculate the distance traveled during the second segment of motion.
The particle then moves with a constant speed of 6 m/s for 3 seconds.
- Distance \( s_2 = \text{speed} \times \text{time} = 6 \, \text{m/s} \times 3 \, \text{s} = 18 \, \text{m} \)

### Step 3: Calculate the total distance traveled.
- Total distance \( s = s_1 + s_2 = 8 \, \text{m} + 18 \, \text{m} = 26 \, \text{m} \)

### Step 4: Calculate the total time taken.
- Total time \( t = t_1 + t_2 = 2 \, \text{s} + 3 \, \text{s} = 5 \, \text{s} \)

### Step 5: Calculate the average speed.
Average speed is defined as total distance divided by total time.
- Average speed \( v_{\text{avg}} = \frac{\text{total distance}}{\text{total time}} = \frac{26 \, \text{m}}{5 \, \text{s}} = 5.2 \, \text{m/s} \)

Thus, the average speed of the particle in the given time interval is **5.2 m/s**.

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