Two particles are `100 m` apart and start approaching each other with constant velocities of `2 m//s and 3 m//s`. The particles will meet after.

Options

A. 20 s
B. 50 s
C. 33.3 s
D. 15 s

Explanation

To solve the problem of when two particles, starting 100 meters apart and moving towards each other with velocities of 2 m/s and 3 m/s, will meet, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the velocities of the particles**:
- Let the velocity of the first particle (Particle A) be \( v_A = 2 \, \text{m/s} \).
- Let the velocity of the second particle (Particle B) be \( v_B = 3 \, \text{m/s} \).

2. **Determine the total distance**:
- The initial distance between the two particles is \( d = 100 \, \text{m} \).

3. **Calculate the relative velocity**:
- Since both particles are moving towards each other, their relative velocity is the sum of their individual velocities:
\[ v_{\text{relative}} = v_A + v_B = 2 \, \text{m/s} + 3 \, \text{m/s} = 5 \, \text{m/s} \]

4. **Set up the equation for time**:
- We know that distance is equal to velocity multiplied by time. Therefore, we can express the time \( t \) it takes for the particles to meet as:
\[ d = v_{\text{relative}} \times t \]
- Substituting the known values:
\[ 100 \, \text{m} = 5 \, \text{m/s} \times t \]

5. **Solve for time \( t \)**:
- Rearranging the equation gives:
\[ t = \frac{100 \, \text{m}}{5 \, \text{m/s}} = 20 \, \text{s} \]

6. **Conclusion**:
- The two particles will meet after \( t = 20 \, \text{seconds} \).

### Final Answer:
The particles will meet after **20 seconds**.

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