The length of the minute hand is the radius of the circular path it traces, r = 7 cm.

Here's how to solve question 16:

The length of the minute hand is the radius of the circular path it traces, $r = 7 \text{ cm}$.
The time interval is from 6 PM to 7:30 PM, which is $1 \text{ hour } 30 \text{ minutes}$, or $90 \text{ minutes}$.
In seconds, $t = 90 \text{ minutes} \times 60 \text{ s/minute} = 5400 \text{ s}$.

Step 1: Determine the initial and final positions of the minute hand.
At 6 PM, the minute hand points to the 12.
At 7:30 PM, the minute hand has completed one full revolution (reaching 7 PM, pointing to 12 again) and then moved another half revolution (30 minutes) to point to the 6.

• a) Distance travelled: The minute hand completes 1.5 revolutions in 90 minutes. The distance for one revolution is the circumference of the circle, $C = 2\pi r$.

  $$C = 2 \times \pi \times 7 \text{ cm} = 14\pi \text{ cm}$$

  Distance travelled for 1.5 revolutions:

  $$D = 1.5 \times 14\pi \text{ cm} = 21\pi \text{ cm}$$ $$D \approx 21 \times 3.14159 \text{ cm} \approx 65.97 \text{ cm}$$

  The distance travelled is $\boxed{\text{21\pi cm or approximately 65.97 cm}}$.

• b) Displacement: The initial position is at the 12 mark. The final position is at the 6 mark. The displacement is the straight-line distance from the initial to the final position. This is the diameter of the circle.

  $$\text{Displacement} = 2r = 2 \times 7 \text{ cm} = 14 \text{ cm}$$

  The displacement is $\boxed{\text{14 cm}}$.

• c) Speed: Speed is the total distance travelled divided by the total time taken.

  $$\text{Speed} = \frac{\text{Distance travelled}}{\text{Time}}$$ $$\text{Speed} = \frac{21\pi \text{ cm}}{90 \text{ minutes}} = \frac{7\pi}{30} \text{ cm/minute}$$ $$\text{Speed} \approx \frac{65.97 \text{ cm}}{90 \text{ minutes}} \approx 0.733 \text{ cm/minute}$$

  In cm/s:

  $$\text{Speed} = \frac{21\pi \text{ cm}}{5400 \text{ s}} = \frac{7\pi}{1800} \text{ cm/s}$$ $$\text{Speed} \approx \frac{65.97 \text{ cm}}{5400 \text{ s}} \approx 0.0122 \text{ cm/s}$$

  The speed is $\boxed{\frac{7\pi}{30} \text{ cm/minute or approximately 0.733 cm/minute}}$.

• d) Velocity: Velocity is the total displacement divided by the total time taken. The direction is from the 12 o'clock position to the 6 o'clock position (downwards).

  $$\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}$$ $$\text{Velocity} = \frac{14 \text{ cm}}{90 \text{ minutes}} = \frac{7}{45} \text{ cm/minute}$$ $$\text{Velocity} \approx \frac{14 \text{ cm}}{90 \text{ minutes}} \approx 0.156 \text{ cm/minute}$$

  In cm/s:

  $$\text{Velocity} = \frac{14 \text{ cm}}{5400 \text{ s}} = \frac{7}{2700} \text{ cm/s}$$ $$\text{Velocity} \approx \frac{14 \text{ cm}}{5400 \text{ s}} \approx 0.00259 \text{ cm/s}$$

  The velocity is $\boxed{\frac{7}{45} \text{ cm/minute downwards or approximately 0.156 cm/minute downwards}}$.