A body of mass m moving along a straight line collides with a body of mass nm which is also moving with a velocity kv in the same direction. If the first body comes to rest after the collision, then the velocity of second body after the collision would be

To find the velocity of the second body after the collision, we can apply the law of conservation of linear momentum. According to this law, the total linear momentum of an isolated system remains constant before and after the collision.

Let us define the initial parameters of the two bodies before the collision:
- Mass of the first body: $m_1=m$
- Initial velocity of the first body: $u_1=v$
- Mass of the second body: $m_2=nm$
- Initial velocity of the second body: $u_2=kv$ (moving in the same direction)

Now, let us define the final parameters of the two bodies after the collision:
- Final velocity of the first body: $v_1=0$ (since it comes to rest)
- Final velocity of the second body: $v_2$ (which we need to find)

Using the law of conservation of linear momentum:
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

Substitute the given values into the equation:
$mv+\left(nm\right)\left(kv\right)=m\left(0\right)+\left(nm\right)v_2$

Simplify the left side and right side of the equation:
$mv(1+nk)=nm{v}_2$

Divide both sides by $m$ (since mass $m\ne 0$):
$v(1+nk)=n{v}_2$

Solve for $v_2$:
$v_2=\frac{(1+nk)v}{n}$

Thus, the velocity of the second body after the collision is $\frac{(1+nk)v}{n}$.