A particle moves in straight line in same direction for 20 seconds with velocity `3 m//s` and the moves with velocity `4 m//s` for another 20 sec and finally moves with velocity `5 m//s` for next 20 seconds. What is the average velocity of the particle?

Options

A. `3 m//s`
B. `4 m//s`
C. `5 m//s`
D. Zero

Explanation

To find the average velocity of the particle, we will follow these steps:

### Step 1: Calculate the distance traveled during each segment of motion.

1. **First Segment**: The particle moves with a velocity of \(3 \, \text{m/s}\) for \(20 \, \text{s}\).
\[ \text{Distance}_1 = \text{Velocity} \times \text{Time} = 3 \, \text{m/s} \times 20 \, \text{s} = 60 \, \text{m} \]

2. **Second Segment**: The particle moves with a velocity of \(4 \, \text{m/s}\) for \(20 \, \text{s}\).
\[ \text{Distance}_2 = 4 \, \text{m/s} \times 20 \, \text{s} = 80 \, \text{m} \]

3. **Third Segment**: The particle moves with a velocity of \(5 \, \text{m/s}\) for \(20 \, \text{s}\).
\[ \text{Distance}_3 = 5 \, \text{m/s} \times 20 \, \text{s} = 100 \, \text{m} \]

### Step 2: Calculate the total distance traveled.

Now, we sum up all the distances:
\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 + \text{Distance}_3 = 60 \, \text{m} + 80 \, \text{m} + 100 \, \text{m} = 240 \, \text{m} \]

### Step 3: Calculate the total time taken.

The total time taken is the sum of the time for each segment:
\[ \text{Total Time} = 20 \, \text{s} + 20 \, \text{s} + 20 \, \text{s} = 60 \, \text{s} \]

### Step 4: Calculate the average velocity.

The average velocity is given by the formula:
\[ \text{Average Velocity} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240 \, \text{m}}{60 \, \text{s}} = 4 \, \text{m/s} \]

### Final Answer:
The average velocity of the particle is \(4 \, \text{m/s}\).

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