Two pulses travel in mutually opposite directions in a string with a speed of `2.5 cm//s` as shown in the figure. Initially the pulses are `10 cm` apart. What will be the state of the string after two seconds?

Options

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Explanation

To solve the problem of determining the state of the string after two seconds, we can follow these steps:

### Step 1: Understand the Initial Conditions
- The two pulses are initially 10 cm apart.
- Each pulse travels at a speed of 2.5 cm/s in opposite directions.

### Step 2: Calculate the Distance Each Pulse Travels in 2 Seconds
- Since the speed of each pulse is 2.5 cm/s, we can calculate the distance traveled by each pulse in 2 seconds using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- For 2 seconds:
\[ \text{Distance} = 2.5 \, \text{cm/s} \times 2 \, \text{s} = 5 \, \text{cm} \]

### Step 3: Determine the New Positions of the Pulses
- Since the pulses are moving towards each other, we need to consider their new positions after 2 seconds.
- The first pulse moves 5 cm towards the second pulse, and the second pulse also moves 5 cm towards the first pulse.

### Step 4: Calculate the New Distance Between the Pulses
- Initially, the distance between the two pulses was 10 cm.
- After 2 seconds, each pulse has moved 5 cm towards each other, so the new distance between the pulses is:
\[ \text{New Distance} = \text{Initial Distance} - (\text{Distance moved by Pulse 1} + \text{Distance moved by Pulse 2}) \]
\[ \text{New Distance} = 10 \, \text{cm} - (5 \, \text{cm} + 5 \, \text{cm}) = 0 \, \text{cm} \]

### Step 5: Conclusion
- After 2 seconds, the two pulses will meet at the same point on the string, resulting in a new state where the distance between them is 0 cm.

### Summary of the Solution
- After 2 seconds, the two pulses will overlap completely at the same point on the string.