A person travelling in a straight line moves with a constant velocity v₁ for certain distance x and with a constant velocity v₂ for next equal distance. The average velocity v is given by the relation    [NEET 2019]

For distance x, the person moves with constant velocity v₁ and for another x distance, he moves with constant velocity of v₂ then
Total distance travelled by the person,
                     D = x + x = 2x
Total time taken to cover that distance,

,                    $T=t_1+t_2=\frac{x}{v_1}+\frac{x}{v_2} \left(\because t=\frac{\text{ Distance }}{\text{ Velocity }}\right)$

Average velocity,

                    $v_{\mathrm{av}}=\frac{\text{ Total distance }}{\text{ Total time }}=\frac{D}{T}$ 

                    $v=\frac{2x}{\frac{x}{v_1}+\frac{x}{v_2}}=\frac{2}{\frac{1}{v_1}+\frac{1}{v_2}} \left(\because v_{\mathrm{av}}=v\right)$

$\Rightarrow$                    $\frac{2}{v}=\frac{1}{v_1}+\frac{1}{v_2}$