A body travels the first half of the total distance with velocity v and second half with v2 calculate avg velocity

v = 2 v₁ v₂ / (v₁ + v₂)

Explanation:

The body travels the first half of the distance with velocity v₁. The time it takes is:

t₁ = (d/2) / v₁

t₁ = d / (2v₁)

Similarly, the body travels the second half with velocity v₂, so the time is:

t₂ = (d/2) / v₂

t₂ = d / (2v₂)

The average velocity is the total displacement over total time:

v = d / t

v = d / (t₁ + t₂)

v = d / (d / (2v₁) + d / (2v₂))

v = d / (d/2 (1/v₁ + 1/v₂))

v = 2 / (1/v₁ + 1/v₂)

v = 2 / ((v₁ + v₂) / (v₁ v₂))

v = 2 v₁ v₂ / (v₁ + v₂)