**Distance moved by the block in 2 seconds**

To find the distance moved by the block in 2 seconds, we need to consider the motion of both the string and the plank. Let's break down the problem step by step.

**Motion of the string**

Given that the string is trapped by a drum fixed in the plank and it moves at a speed of 1 centimeter per second. We can calculate the distance moved by the string in 2 seconds using the formula:

Distance = Speed × Time

Distance = 1 cm/s × 2 s = 2 cm

So, the string moves a distance of 2 centimeters in 2 seconds.

**Motion of the plank**

The plank is moving downward with a speed of 2 centimeters per second. To calculate the distance moved by the plank in 2 seconds, we again use the formula:

Distance = Speed × Time

Distance = 2 cm/s × 2 s = 4 cm

Therefore, the plank moves a distance of 4 centimeters in 2 seconds.

**Total distance moved by the block**

To find the total distance moved by the block, we need to consider the motion of both the string and the plank. Since the string is trapped by the drum fixed in the plank, the movement of the string is directly transferred to the block.

In 2 seconds, the string moves 2 centimeters and the plank moves 4 centimeters. Since the block is attached to the string, it will move the same distance as the string.

Therefore, the block will also move a distance of 2 centimeters in 2 seconds.

**Conclusion**

In conclusion, the block will move a distance of 2 centimeters in 2 seconds. This is because the string, which is trapped by the drum fixed in the plank, moves 2 centimeters in 2 seconds, and the block moves the same distance as the string. Additionally, the plank's downward motion does not affect the distance moved by the block.