consider a head on collision between two particles of masses `m_1 and m_2`. The initial speeds of the particles are `u_1 and u_2` in the same direction. The collision starts at t=0 and the particles interact for a time interval `/_\t.` during the collision the speed of the first particle varies as
`v(t)=u_1+t//_\ t(v_1-u_1)` Find the speed of the second particle as as function of time during the collision.

Explanation

To find the speed of the second particle as a function of time during the collision, we will apply the principle of conservation of linear momentum. Here are the steps to derive the expression for the speed of the second particle, \( v_2(t) \):

### Step-by-Step Solution:

1. **Identify the Initial Momentum**:
The initial momentum of the system before the collision is given by:
\[
P_{\text{initial}} = m_1 u_1 + m_2 u_2
...