(C) Let the total distance of the journey be $2d$. Time taken for the first half of the journey is $t_1 = \frac{d}{v_1}$. Time taken for the second ha

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(C) Let the total distance of the journey be $2d$. Time taken for the first half of the journey is $t_1 = \frac{d}{v_1}$. Time taken for the second half of the journey is $t_2 = \frac{d}{v_2}$. Average velocity $V_{av} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2d}{t_1 + t_2}$. Substituting the values,$V_{av} = \frac{2d}{\frac{d}{v_1} + \frac{d}{v_2}} = \frac{2d}{d(\frac{v_2 + v_1}{v_1 v_2})} = \frac{2v_1 v_2}{v_1 + v_2}$.

Class 11 Mathematics Sequences and Series Relation between A.P., G.P.

Medium

$A$ car completes the first half of its journey with a velocity $v_1$ and the rest half with a velocity $v_2$. Then the average velocity of the car for the whole journey is

A
$\frac{v_1 + v_2}{2}$
B
$\sqrt{v_1 v_2}$
C
$\frac{2v_1 v_2}{v_1 + v_2}$
D
None of these

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Relation between A.P., G.P.

Suppose $a, b, c$ are in $A.P.$ and $a^{2}, 2b^{2}, c^{2}$ are in $G.P.$ If $a < b < c$ and $a+b+c=1,$ then $9(a^{2}+b^{2}+c^{2})$ is equal to . . . . . . .

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If $9$ arithmetic means $(A.M.s)$ and $9$ harmonic means $(H.M.s)$ are inserted between $2$ and $3$,and if the harmonic mean $H$ corresponds to the arithmetic mean $A$ (i.e.,the $j^{th}$ $A.M.$ and $j^{th}$ $H.M.$),then $A + \frac{6}{H} = $

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If $p^{\text{th}}, q^{\text{th}}, r^{\text{th}},$ and $s^{\text{th}}$ terms of an $A.P.$ are in $G.P.,$ then show that $(p-q), (q-r),$ and $(r-s)$ are also in $G.P.$

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If $a, b, c$ are any three positive numbers,then what is the minimum value of $(a + b + c) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$?

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If the arithmetic mean of two positive numbers is $A$,their geometric mean is $G$,and their harmonic mean is $H$,then $H$ is equal to:

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$A$ car completes the first half of its journey with a velocity $v_1$ and the rest half with a velocity $v_2$. Then the average velocity of the car for the whole journey is

Similar Questions

Suppose $a, b, c$ are in $A.P.$ and $a^{2}, 2b^{2}, c^{2}$ are in $G.P.$ If $a < b < c$ and $a+b+c=1,$ then $9(a^{2}+b^{2}+c^{2})$ is equal to . . . . . . .

If $9$ arithmetic means $(A.M.s)$ and $9$ harmonic means $(H.M.s)$ are inserted between $2$ and $3$,and if the harmonic mean $H$ corresponds to the arithmetic mean $A$ (i.e.,the $j^{th}$ $A.M.$ and $j^{th}$ $H.M.$),then $A + \frac{6}{H} = $

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If $a, b, c$ are any three positive numbers,then what is the minimum value of $(a + b + c) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$?

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