Question

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:

1. distance travelled,
2. displacement,
3. speed, and
4. velocity.

The length of the minute’s hand is 7 cm (Fig.).

Answer 1

Given Data:

Length of minute hand (r): 7cm

Time interval: 6:00 PM to 7:30 PM = 90 mins = 5400 s

Rotations: In 90 minutes, the hand completes 1.5 circles.

(i) Distance travelled

Distance covered in one revolution = circumference = 2πr

= `2 xx 22/7 xx 7`

= 44 cm

∴ Distance in 1.5 revolutions = 44 × 1.5 = 66 cm

(ii) Displacement

The tip is at 12 o’clock at 6:00 PM. The tip hits the 6 mark, which is completely different from the initial position, after 1.5 rotations.

∴ Displacement = circle diameter = 2r = 2 × 7 = 14 cm
(pointed vertically downward from the starting location)

(iii) Speed

Time = 90 minutes = 90 × 60 = 5400 s

Speed = `"distance"/"time"`

= `66/5400`

= 0.0122 cm s^–1 (approximately)

(iv) Velocity

Velocity = `"displacement"/"time"`

= `14/5400`

= 0.0026 cm s^–1 (approximately) directed from the initial position (12) towards the final position (6).