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 of finding the average acceleration of a particle moving along a circular path while speeding up uniformly between two diametrically opposite points, we can follow these steps:

### Step 1: Understand the motion
The particle moves along a circular path of radius \( R \) and travels between two diametrically opposite points. The distance covered in this motion is half the circumference of the circle.

### Step 2: Calculate the distance
The total circumference \( C \) of the circle is given by:
\[
...