A particle covers half of its total distance | vedclass

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Question

${\upsilon _{av}} = \frac{{{d_1} + {d_2}}}{{\frac{{{d_1}}}{{{\upsilon _1}}} + \frac{{{d_2}}}{{{\upsilon _2}}}}}$= $\frac{{\frac{d}{2} + \frac{d}{2}}}{

Vedclass · Accepted Answer

$\;$ $\frac{{2{v_1}{v_2}}}{{{v_1} + {v_2}}}$

Vedclass · Answer

${\upsilon _{av}} = \frac{{{d_1} + {d_2}}}{{\frac{{{d_1}}}{{{\upsilon _1}}} + \frac{{{d_2}}}{{{\upsilon _2}}}}}$= $\frac{{\frac{d}{2} + \frac{d}{2}}}{{\frac{{d/2}}{{{\upsilon _1}}} + \frac{{d/2}}{{{\upsilon _2}}}}}$

$\Rightarrow {\upsilon _{av}} = \frac{2}{{\frac{1}{{{\upsilon _1}}} + \frac{1}{{{\upsilon _2}}}}}$ = $\frac{{2{\upsilon _1}\,{\upsilon _2}}}{{{\upsilon _1} + {\upsilon _2}}}$

A particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2 .$ Its average speed during the complete journey is

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