In one dimensional elastic collison of equla masses, the velocities are interchanged. Can velocities ina one dimensional collision be interchanged if the masses are not equal?

Explanation

To determine whether the velocities can be interchanged in a one-dimensional elastic collision when the masses are not equal, we can analyze the situation using the principles of conservation of momentum and conservation of kinetic energy.

### Step 1: Define the Problem
We have two masses, \( m_1 \) and \( m_2 \), with initial velocities \( u_1 \) and \( u_2 \) respectively. We want to find out if, after an elastic collision, the final velocities \( v_1 \) and \( v_2 \) can be equal to \( u_2 \) and \( u_1 \) respectively (i.e., if the velocities can be interchanged).

**Hint:** Start by recalling the definitions of elastic collision and the conservation laws.

### Step 2: Apply Conservation of Momentum
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