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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 \(\dfrac{90}{60} = 1.5\) revolutions. Radius \(R = 7\ \text{cm}\).
(i) Distance \(= 1.5 \times 2\pi R = 1.5 \times 2 \times \tfrac{22}{7} \times 7 = 1.5 \times 44 = 66\ \text{cm}\).
(ii) After 1.5 turns the tip is diametrically opposite its start, so displacement \(= 2R = 14\ \text{cm}\).
(iii) Speed \(= \dfrac{66\ \text{cm}}{90\ \text{min}} \approx 0.73\ \text{cm min}^{-1}\) (i.e. 44 cm h⁻¹).
(iv) Velocity \(= \dfrac{14\ \text{cm}}{90\ \text{min}} \approx 0.16\ \text{cm min}^{-1}\), directed from the start position to the end position.
