A particle traversed a third of the distance with a velocity of v₀. The remaining part of the distance was covered with velocity v₁ for half the time and with velocity v₂ for the remaining half of the time. Assuming motion to be rectilinear, find the mean velocity of the particle averaged over the whole time of motion.

For AC; (S/3) = v₀t₁ → t₁ = S/(3v₀) ....(1)

For CB; (2S/3) = CD + DB

Since, average velocity is defined as