Motion in a Straight Line - Result Question 1
1. A person travelling in a straight line moves with a constant velocity $v_1$ for certain distance ’ $x$ ’ and with a constant velocity $v_2$ for next equal distance. The average velocity $v$ is given by the relation
[NEET Odisha 2019]
(a) $v=\sqrt{v_1 v_2}$
(b) $\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}$
(c) $\frac{2}{v}=\frac{1}{v_1}+\frac{1}{v_2}$
(d) $\frac{v}{2}=\frac{v_1+v_2}{2}$
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Solution:
- (c) As $t_1 \frac{x}{v_1}=$ and $t_2=\frac{x}{v_2}$
$\therefore \quad v=\frac{x+x}{t_1+t_2}=\frac{2 x}{\frac{x}{v_1}+\frac{x}{v_2}}=\frac{2 v_1 v_2}{v_1+v_2}$
$\therefore \quad \frac{2}{v}=\frac{1}{v_1}+\frac{1}{v_2}$
