A person travels along a straight road for the first half time with a velocity \(v_{1}\) and the second half…

A person travels along a straight road for the first half time with a velocity \(v_{1}\) and the second half time with a velocity \(v_{2}\). Then the mean velocity \(\bar{v}\) is given by
  1. \(\bar{v}=\frac{v_{1}+v_{2}}{2}\)
  2. \(\frac{2}{\bar{v}}=\frac{1}{v_{1}}+\frac{1}{v_{2}}\)
  3. \(\bar{v}=\sqrt{v_{1} v_{2}}\)
  4. \(\bar{v}=\sqrt{\frac{v_{2}}{v_{1}}}\)

Solution

\(V_{\mathrm{av}}=\frac{v_{1}(t / 2)+v_{2}(t / 2)}{t}=\frac{v_{1}+v_{2}}{2}\)

Asked in: JEE Mains - Motion In One Dimension - Chapter Test

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