A particle traversed half of the distance with a velocity of `V_(0)`.The remaining parts of the distance was covered with velocity `V_(1)`, for half of the time and with `V_(2)` for other half of the time .Find the mean velocity of the particle averahed and the whole time of motion .

Explanation

To find the mean velocity of the particle over the whole time of motion, we can break down the problem into steps:

### Step 1: Define the total distance and distances covered
Let the total distance be \( S \). The particle travels half of this distance, \( \frac{S}{2} \), with a velocity \( V_0 \). The remaining half, \( \frac{S}{2} \), is covered in two parts: half the time with velocity \( V_1 \) and the other half with velocity \( V_2 \).

### Step 2: Calculate the time taken for the first half of the distance
The time taken to cover the first half of the distance is given by:
\[
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