Final answer:
After 30 seconds, a bug on a clock's second hand that rotates uniformly in a circle has a vector displacement equal to the diameter of the circular path, which is 40 centimeters.
Step-by-step explanation:
If a bug at the tip of a clock's second hand that is 20 centimeters long moves at a speed of 0.5 cm/s, after 30 seconds, we need to calculate the bug's vector movement in centimeters. A vector quantity has both magnitude and direction. Considering the clock's second hand rotates uniformly in a circular path, the magnitude of displacement after 30 seconds is the straight-line distance between the bug's starting and final positions. The direction is given by the line joining these two positions.
To find this displacement vector, we need to realize that 30 seconds represents half the period of revolution of the clock's second hand, which means the bug will be on the opposite end of the dial directly through the center. The magnitude of the displacement is thus the diameter of the circle described by the tip of the second hand, which is 20 cm + 20 cm = 40 cm. The bug's vector movement is hence 40 centimeters along the diameter from the original position.