Two particles A and B start moving simultaneously along the line joining them in the same direction with acceleration of `1 m//s^2 and 2 m//s^2` and speeds `3 m//s and 1 m//s` respectively. Initially, A is 10 m behind B. What is the minimum distance between them?

Explanation

To solve the problem of finding the minimum distance between particles A and B, we can follow these steps:

### Step 1: Understand the Initial Conditions
- Particle A has an initial velocity \( u_A = 3 \, \text{m/s} \) and an acceleration \( a_A = 1 \, \text{m/s}^2 \).
- Particle B has an initial velocity \( u_B = 1 \, \text{m/s} \) and an acceleration \( a_B = 2 \, \text{m/s}^2 \).
- Initially, particle A is 10 meters behind particle B.

### Step 2: Set Up the Equations for Final Velocities
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