Question

If a body travels half the distance with velocity ${{v}_{1}}$ and the next half with velocity ${{v}_{2}}$ its average velocity will be given by

• A. $v=\sqrt{{{v}_{1}}{{v}_{2}}}$
• B. $v=\frac{{{v}_{1}}+{{v}_{1}}}{2}$
• C. $v=\frac{{{v}_{1}}}{{{v}_{2}}}$
• D. $\frac{2}{v}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}$

Answer 1

Answer: (D)

$\frac{2}{v}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}$

Answer 2

Average velocity $=\frac{total\text{ }distance\text{ }travelled}{total\text{ }time\text{ }taken}$ Let the total distance $=d$ . $\therefore$ $v=\frac{d}{\frac{d}{2{{v}_{1}}}+\frac{d}{{{v}_{2}}}}$ $v=\frac{d}{\frac{d}{2}\left( \frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}} \right)}$ Or $v=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}$ Or $\frac{{{v}_{1}}+{{v}_{2}}}{{{v}_{1}}{{v}_{2}}}=\frac{2}{v}$ Or $\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}=\frac{2}{v}$