question_answer

A man travelling in a straight line moves with a uniform velocity \[{{v}_{1}}\]for a certain distance and with a uniform velocity \[{{v}_{2}}\]for the next equal distance. Find the average velocity (v).

Answer:

\[=\frac{1}{4}\times 2\pi r=\frac{\pi r}{2}\] since\[{{s}_{1}}\frac{s}{2}\And {{s}_{2}}=\frac{s}{2}\]and \[{{t}_{1}}=\frac{s/2}{{{V}_{1}}}\And {{t}_{2}}\frac{s/2}{{{V}_{2}}}\] \[{{V}_{ave}}=\frac{s}{\frac{s/r}{{{v}_{1}}}+\frac{s/2}{{{v}_{2}}}}=\frac{s}{\left[ \frac{1}{2{{v}_{1}}}+\frac{1}{{{v}_{2}}} \right]}\] \[=\frac{4{{v}_{1}}{{v}_{2}}}{2[{{v}_{1}}+{{v}_{2}}]}=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\] or \[\frac{2}{v}=\frac{{{v}_{1}}+{{v}_{2}}}{{{v}_{1}}{{v}_{2}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}\]