Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute's hand of the wall clock. During the given time interval, what is its:

(A) distance travelled,

(B) displacement,

(C) speed, and

(D) velocity.

The length of the minute's hand is 7 cm as shown in the given figure:

Time interval = 6 PM to 7:30 PM = 1.5 hours = 90 min = 5400 s;

Length of minute's hand (radius) R = 7 cm

In 90 minutes, the minute's hand completes 1.5 revolutions (60 min = 1 revolution).

$$\text{Circumference} = 2\pi R = 2 \times \frac{22}{7} \times 7 = 44 \text{ cm}$$

(A) Distance travelled:

$$d = 1.5 \times 2\pi R = 1.5 \times 44 = 66 \text{ cm}$$

(B) Displacement:

After 1.5 revolutions, the tip ends up diametrically opposite to its starting position ($\frac{1}{2}$ revolution extra).

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

(C) Speed:

$$\begin{aligned} \text{Speed} &= \frac{\text{Distance}}{\text{Time}} \\ &= \frac{66 \text{ cm}}{5400 \text{ s}} \approx 0.0122 \text{ cm/s} \end{aligned}$$

(D) Velocity:

$$\begin{aligned} \text{Velocity} &= \frac{\text{Displacement}}{\text{Time}} \\ &= \frac{14 \text{ cm}}{5400 \text{ s}} \approx 2.59 \times 10^{-3} \text{ cm/s} \end{aligned}$$

Directed along the diameter (from initial to final position of the tip).