Q122 / 160 · AP EAMCET 2023 (17 May Shift 2) · Physics

If a person moving along a straight line path covers first half distance with velocity ' $\mathrm{V}_1$ ' and the next half distance with velocity ' $\mathrm{V}_2$ ', then the average velocity of the person is

  • A
    $\frac{V_1+V_2}{2}$
  • B
    $\frac{\left(V_1+V_2\right)}{2 \sqrt{V_1 V_2}}$
  • Correct answer
    C
    $\frac{2}{\frac{1}{V_1}+\frac{1}{V_2}}$
  • D
    $\frac{V_1 V_2}{V_1+V_2}$

Solution

Time taken for the first half distance is $t_1=\frac{d}{2 v_1}$ Time taken for the second half distance is $t_2=\frac{d}{2 v_2}$ Average velocity $=\frac{\text { Total distance }}{\text { Total time }}$ $\begin{aligned} & =\frac{d}{t_1+t_2}=\frac{d}{\frac{d}{2 v_1}+\frac{d}{2 v_2}} \\ & =\frac{1}{\frac{v_1+v_2}{2 v_1 v_2}}=\frac{2 v_1 v_2}{v_1+v_2}\end{aligned}$

Hence, the correct answer is option: 'C'.

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