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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: (i) distance travelled, (ii) displacement, (iii) speed, and (iv) velocity. The length of the minute’s hand is 7 cm (Fig. 4.32).
Show Answer
6:00 to 7:30 = 90 min = 1.5 h. The minute hand makes 90 60 = 1.5 revolutions. Radius R = 7 cm .
(i) Distance = 1.5 × 2π R = 1.5 × 2 × 22 7 × 7 = 1.5 × 44 = 66 cm .
(ii) After 1.5 turns the tip is diametrically opposite its start, so displacement = 2R = 14 cm .
(iii) Speed = 66 cm 90 min ≈ 0.73 cm min -1 (i.e. 44 cm h⁻¹).
(iv) Velocity = 14 cm 90 min ≈ 0.16 cm min -1 , directed from the start position to the end position.
| Quantity | Value |
|---|---|
| Distance | 66 cm |
| Displacement | 14 cm |
| Speed | ≈ 0.73 cm/min |
| Velocity | ≈ 0.16 cm/min |
