A car travels a distance of x with speed v _ 1 and then same...

Average velocity of car is:

${v}_{avg} = \dfrac{\text{Total displacement}}{\text{Total time}}$

As the car is travelling along a straight line without turning, the magnitude of total displacement is same as the distance covered.

The time taken to cover the first half is $\dfrac{x}{{v}_{1}}$ and the time taken to cover the second half is $\dfrac{x}{{v}_{2}}$

$∴ {v}_{avg} = \dfrac{2x}{\dfrac{x}{{v}_{1}} + \dfrac{x}{{v}_{2}}}$

$⇒ {v}_{avg} = \dfrac{2x\left({v}_{1}{v}_{2}\right)}{{v}_{1}x + {v}_{2}x} = \dfrac{2{v}_{1}{v}_{2}}{{v}_{1} + {v}_{2}}$