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In 1.0 s, a particle goes from point A t...

In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m. The magnitude of the average velocity is :-

A

3.14 m/s

B

2.0 m/s

C

1.0 m/s

D

zero

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The correct Answer is:
To solve the problem of finding the magnitude of the average velocity of a particle moving from point A to point B along a semicircle of radius 1.0 m in 1.0 s, we can follow these steps: ### Step 1: Understand the motion The particle moves along a semicircular path. The radius of the semicircle is given as 1.0 m. ### Step 2: Calculate the displacement Displacement is the straight-line distance from the initial point (A) to the final point (B). Since the particle moves along a semicircle, the displacement will be the diameter of the semicircle. The diameter \(d\) of a semicircle is given by: \[ d = 2 \times \text{radius} = 2 \times 1.0 \, \text{m} = 2.0 \, \text{m} \] ### Step 3: Calculate the time taken The time taken for the particle to move from point A to point B is given as 1.0 s. ### Step 4: Calculate the average velocity The average velocity \(v_{avg}\) is defined as the total displacement divided by the total time taken. Thus, \[ v_{avg} = \frac{\text{displacement}}{\text{time}} = \frac{2.0 \, \text{m}}{1.0 \, \text{s}} = 2.0 \, \text{m/s} \] ### Final Answer The magnitude of the average velocity is \(2.0 \, \text{m/s}\). ---
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