A person travelling on a straight line moves with a uniform velocity \(\mathrm{v}_1\) for a distance x and with a uniform velocity \(\mathrm{v}_2\) for the next \(\frac{3}{2} \mathrm{x}\) distance. The average velocity in this motion is \(\frac{50}{7} \mathrm{~m} / \mathrm{s}\). If \(\mathrm{v}_1\) is \(5 \mathrm{~m} / \mathrm{s}\) then \(\mathrm{v}_2=\) _________ \(\mathrm{m} / \mathrm{s}\).

\(\begin{aligned} & \mathrm{v}_{\text {avg }}=\frac{\mathrm{x}_1+\mathrm{x}_2}{\mathrm{t}_1+\mathrm{t}_2} \\ & \Rightarrow \frac{50}{7}=\frac{\mathrm{x}+\frac{3 \mathrm{x}}{2}}{\frac{\mathrm{x}}{5}+\frac{3 \mathrm{x}}{2 \mathrm{v}_2}} \\ & \Rightarrow \frac{50}{7}=\frac{5 / 2}{\frac{1}{5}+\frac{3}{2 \mathrm{v}_2}} \\ & \Rightarrow \frac{1}{5}+\frac{3}{2 \mathrm{v}_2}=\frac{7}{20}\end{aligned}\)
\(\begin{aligned} & \Rightarrow \frac{3}{2 \mathrm{v}_2}=\frac{7}{20}-\frac{1}{5}=\frac{7-4}{20} \\ & \Rightarrow \frac{3}{2 \mathrm{v}_2}=\frac{3}{20} \\ & \Rightarrow \mathrm{v}_2=10 \mathrm{~m} / \mathrm{s}\end{aligned}\)