Question

An ant goes from P to Q on a circular path in 20 second Radius OP = 10m. What is the average speed and average velocity of it ? 

(A) (π/6) ms^–1, 3 ms^–1 

(B) (π/3) ms^–1, (√3 / 2) ms^–1 

(C) (π/3) ms^–1, √3 ms^–1 

(D) π ms^–1, √6 ms^–1

Answer 1

Correct option: (B) (π/3)ms^–1, (√3 / 2)ms^–1

Explanation:

Draw OS ⊥ PQ 

Δ OSQ is 30° – 60° – 90° triangle 

sin 60 = (QS / OQ) 

QS = (√3 / 2) × OQ = (√3 / 2) × 10 = 5√3 m 

l(PQ) = l(PS) + l(SQ) = 10√3 

average speed = {(distance travelled) / (time)}; 

average velocity = {(displacement) / (time)} 

also arc PQ = radius × Q 

= 10 × 120° = 10 × (2π / 3) as 120° 

= (2π / 3) = {(20 π) / 3} 

∴ avg. speed = {(arc PQ) / (time)} 

= [{(20 π) / 3} / {20}] 

= (π/3) m/s 

avg. velocity = {(displacement PQ) / (time)} 

= [{l(PQ)} / {time}] 

= [{10√3} / {20}] 

= (√3 / 2) m/s