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…

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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 $\mathrm{v}_2=$ _________ $\mathrm{m} / \mathrm{s}$.

Aicharya · Accepted Answer

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

A person travelling on a straight line moves with a uniform velocity $\mathrm{v}_1$ for a distance x and…

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