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

The Correct Option is D

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} $