Physics Question from JEE Main 2025 · 2 April, Shift 1

A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\frac{3}{2}x$ distance. The average velocity in this motion is $\frac{50}{7} \, \text{m/s}$. If $v_1$ is $5 \, \text{m/s}$, then $v_2$ is _____ $\text{m/s}$.