1. Given data

• Mass of smaller body: $m_1 = 1\,\text{kg}$
• Mass of larger body: $m_2 = 3\,\text{kg}$
• Initially, larger body is stationary: $u_2 = 0$
• Let initial speed of smaller body be $u_1 = u$
• After collision, smaller body reverses direction with speed $2\,\text{m/s}$, so $v_1 = -2\,\text{m/s}$

Since the collision is elastic, we can use the standard result for 1D elastic collision:

$v_1 = \frac{m_1-m_2}{m_1+m_2}u_1 + \frac{2m_2}{m_1+m_2}u_2$

Because $u_2=0$, this becomes

$v_1 = \frac{m_1-m_2}{m_1+m_2}u_1$

2. Substitute values

$-2 = \frac{1-3}{1+3}u$

$-2 = \frac{-2}{4}u$

$-2 = -\frac{1}{2}u$

3. Solve for $u$

$u = 4\,\text{m/s}$

4. Final answer

The initial speed of the smaller body was

$\boxed{4}$

ms$^{-1}$.