A particle in a circular path speeds up with a uniform rate between two diametrically opposite points of a circle of radius `R`. If its time of motion between these two points is equal to `T`, find the accelertaion of the particle averaged over the time `T`.

Explanation

To solve the problem, we need to find the average acceleration of a particle moving along a circular path while speeding up uniformly between two diametrically opposite points on the circle. The radius of the circle is \( R \) and the time taken to move between these points is \( T \).

### Step-by-Step Solution:

1. **Understand the Motion**:
The particle moves from one point to the diametrically opposite point, covering half the circumference of the circle. The distance covered is:
\[
s = \pi R
...