Average Velocity formula for equal distance intervals (with derivation)

In this post, we will derive the Average Velocity formula for equal distance intervals. In this specific case, a body travels equal distance intervals with different velocities, and we need to find out the average velocity and its formula.

Let’s see what this actually means and what is the formula.

Say, an object is moving from A to B (see Figure 1). The distance between A and B = AB = L meter

Say, this distance L is made of n number of equal distances each of length l meter.

So, we can write L = nl ………………………. (1)

Say the object passes these equal distances with different velocities like v₁, v₂, v₃,…., and v_n.
So total time required to cross the entire distance T = t1 + t2 + t3 +…. + tn = l/v₁ + l/v₂ + ….+ l/v_n
=> T = l [1/v₁ + 1/v₂ + ….+ 1/v_n ] ………………………. (2)

Average Velocity for equal distance intervals = L/T = nl / l [1/v₁ + 1/v₂ + ….+ 1/v_n ]
V_avg = n/[1/v₁ + 1/v₂ + ….+ 1/v_n ]

When n =2
then V_avg = 2/[1/v₁ + 1/v₂] =2v₁ v₂ /[v₁ + v₂]