A monoatomic gas of molar mass m is kept in a insulated container....

Let the insulated container has $n$ moles of the monoatomic gas. The loss of kinetic energy of the gas,
$\Delta E_K=\frac{1}{2}(m n) v^2$
If the change in temperature of the gas is $\Delta T$, then heat gained by the gas is,
$\Delta Q=\frac{3}{2} n R \Delta T$
Now, according to question,
$$\begin{aligned}<br />\Delta Q & =\Delta E_K \\<br />\frac{3}{2} n R \Delta T & =\frac{1}{2} m n v^2 \\<br />\Rightarrow \quad \Delta T & =\frac{m v^2}{3 R}<br />\end{aligned}$$