A particle `A` is moving in `xy` plane with the constant speed of `2pi m//s` along the path `x^(2)+y^(2)+120y=0`. At time `t=0`. When `A` is at the origin, another particle `B` starts moving from origin with constant acceleration is such a way that at time `t=5s` velocities of both the particles are found to be equal. If sense of motion of `A` is clockwise, calculate the average speed of `B` over first five second.

Options

A. `2pi m//s`
B. `pi m//s`
C. `2 m//s`
D. `1 m//s`

Explanation

To solve the problem step by step, we will analyze the motion of both particles A and B, and calculate the average speed of particle B over the first five seconds.

### Step 1: Understand the path of particle A
The equation of the path of particle A is given as:
\[ x^2 + y^2 + 120y = 0 \]
This can be rearranged to:
\[ x^2 + (y + 60)^2 = 60^2 \]
This represents a circle with center at (0, -60) and radius 60 meters.
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