Question

Consider the motion of the tip of the minute hand of a clock. In one hour:
A) The displacement is zero
B) The distance covered is zero
C) The average speed is zero
D) The average velocity is zero

Answer 1

We must know the definition of Displacement, Distance, Average Speed and Average Velocity. We must also know the behavior of the minute hand of a clock, i.e. what happens to the minute hand of the clock after an hour.

Complete step by step solution:
We know that displacement is defined as the difference of the final position vector and the initial position vector. The distance is defined as the total length moved by an object in the course of time. The average speed is defined as total distance covered per total unit time. The average velocity is defined as the total displacement per total unit time.

For the minute hand of the clock, the hand of the clock gets back to its original position after one hour. Therefore, final and initial position vectors are the same. Hence, the displacement is zero. Option A is correct.

The distance covered by the minute hand of the clock will be $2\pi R$, $R$ being the length of the minute hand. Hence, option B is wrong.
The Average speed of the minute hand of the clock will be: ${{v}_{avg}}=\dfrac{2\pi R}{3600}m/s$

Hence, option (C) is wrong.

The average velocity of the minute hand of the clock will be: ${{\vec{v}}_{avg}}=\dfrac{{\vec{0}}}{3600}m/s=\vec{0}m/s$

Hence, option (D) is correct.

Therefore, options (A) and (D) are correct.

Note: When you are writing in an exam, don’t forget to write the vector symbol wherever required. Take note of the units mentioned and scale them down to a single unit. We must not confuse between distance and displacement, speed and velocity.