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Home » A person travelling in a straight line moves with a constant velocity for certain distance and with a constant velocity for next equal distance. The average velocity is given by the relation (1) (2) (3) (4)
A person travelling in a straight line moves with a constant velocity v_{1} for certain distance { }^{\prime} \mathrm{x}^{3} and with a constant velocity v_{2} for next equal distance. The average velocity v is given by the relation (1) v=\sqrt{v_{1} v_{2}} (2) \frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} (3) \frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} (4) \frac{v}{2}=\frac{v_{1}+v_{2}}{2}
Physics | Physics
A person travelling in a straight line moves with a constant velocity v_{1} for certain distance { }^{\prime} \mathrm{x}^{3} and with a constant velocity v_{2} for next equal distance. The average velocity v is given by the relation (1) v=\sqrt{v_{1} v_{2}} (2) \frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} (3) \frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} (4) \frac{v}{2}=\frac{v_{1}+v_{2}}{2}

Answer (3)
Sol.
As t_{1}=\frac{x}{v_{1}} and t_{2}=\frac{x}{v_{2}}
\begin{array}{l} \therefore \quad v=\frac{x+x}{t_{1}+t_{2}} \\ \qquad=\frac{2 x}{\frac{x}{v_{1}}+\frac{x}{v_{2}}}=\frac{2 v_{1} v_{2}}{v_{1}+v_{2}} \\ \therefore \quad \frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} \end{array}

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