A table clock has its minute hand 5.0 cm long`. The average velocity of the tip of the minute hand between ` 6.00 am` to ` 6.30 pm` is.

Answer

To solve the problem of finding the average velocity of the tip of the minute hand of a clock from 6:00 AM to 6:30 PM, we can follow these steps:

### Step 1: Identify the length of the minute hand
The length of the minute hand is given as 5.0 cm. This length will be used as the radius (R) in our calculations.

### Step 2: Determine the initial and final positions of the minute hand
- At 6:00 AM, the minute hand points at the 12 o'clock position.
- At 6:30 PM, the minute hand points at the 6 o'clock position.

### Step 3: Calculate the displacement
The displacement is the straight-line distance between the initial and final positions of the minute hand.
- The initial position (at 6:00 AM) is at the top (12 o'clock), and the final position (at 6:30 PM) is at the bottom (6 o'clock).
- The distance between these two points is equal to the diameter of the circle traced by the minute hand, which is \(2R\).
- Since \(R = 5.0 \, \text{cm}\), the displacement is:
\[ \text{Displacement} = 2R = 2 \times 5.0 \, \text{cm} = 10.0 \, \text{cm} \]

### Step 4: Calculate the total time taken
The total time from 6:00 AM to 6:30 PM is:
- From 6:00 AM to 6:00 PM is 12 hours.
- From 6:00 PM to 6:30 PM is an additional 30 minutes.
- Therefore, the total time is:
\[ \text{Total time} = 12 \, \text{hours} + 0.5 \, \text{hours} = 12.5 \, \text{hours} \]

### Step 5: Calculate the average velocity
Average velocity is defined as total displacement divided by total time taken.
- We convert the displacement from centimeters to meters for standard units:
\[ \text{Displacement in meters} = 10.0 \, \text{cm} = 0.1 \, \text{m} \]
- Now, we can calculate the average velocity:
\[ \text{Average velocity} = \frac{\text{Total displacement}}{\text{Total time}} = \frac{0.1 \, \text{m}}{12.5 \, \text{hours}} \]
- To convert hours to seconds (1 hour = 3600 seconds):
\[ \text{Total time in seconds} = 12.5 \times 3600 = 45000 \, \text{seconds} \]
- Now substituting this into the average velocity formula:
\[ \text{Average velocity} = \frac{0.1 \, \text{m}}{45000 \, \text{s}} \approx 2.22 \times 10^{-6} \, \text{m/s} \]

### Final Answer
The average velocity of the tip of the minute hand between 6:00 AM to 6:30 PM is approximately \(2.22 \times 10^{-6} \, \text{m/s}\).

---