Question

a particle is moving in a circular path of radius 1 m with a constant speed of root2 pai m/s . the average velocity of particle from A to B​

Answer 1

first find time taken to complete one revolution.

t = distance covered in complete revolution/speed of particle

= 2π(1m)/√2π m/s

= √2 s

as time taken to complete one rotation = √2 s

so, time taken for 1/4th rotation , t' = √2/4 = 1/2√2 s

now, average velocity of particle from A to B = displacement from A to B/time taken

= hypotenuse AB/(1/2√2s)

= √(1² + 1²) × 2√2 m/ s

= √2 × 2√2 m/s

= 4m/s

hence, option (2) is correct choice.

Answer 2

$\huge\bold\purple{Answer:-}$

first find time taken to complete one revolution.

t = distance covered in complete revolution/speed of particle

= 2π(1m)/√2π m/s

= √2 s

as time taken to complete one rotation = √2 s

so, time taken for 1/4th rotation , t' = √2/4 = 1/2√2 s

now, average velocity of particle from A to B = displacement from A to B/time taken

= hypotenuse AB/(1/2√2s)

= √(1² + 1²) × 2√2 m/ s

= √2 × 2√2 m/s

= 4m/s