Answer:
[tex]v=\frac{v_{1}v_{2}}{\left ( v_{1}+v_{2} \right )}[/tex]
Explanation:
Let the distance traveled in first half is d and then in the next half is also d.
Let the time taken in first half is t1 and the time taken in the second half is t2.
[tex]t_{1}=\frac{d}{v_{1}}[/tex]
[tex]t_{2}=\frac{d}{v_{2}}[/tex]
Total time taken
[tex]t=t_{1}+t_{2}=\frac{d}{v_{1}}+\frac{d}{v_{2}}=\frac{d\left ( v_{1}+v_{2} \right )}{v_{1}v_{2}}[/tex]
The average speed of a body is defined as the total distance traveled by teh body to the total time taken.
[tex]Average speed = \frac{total distance}{total time}[/tex]
[tex]v=\frac{2d}{t}[/tex]
[tex]v=\frac{2d}{\frac{2d\left ( v_{1}+v_{2} \right )}{v_{1}v_{2}}}[/tex]
[tex]v=\frac{v_{1}v_{2}}{\left ( v_{1}+v_{2} \right )}[/tex]
