A particle has to cover a total distance D. It covers the first D/3 with speed v. The remaining distance is covered in two equal time intervals with speeds 2v and 3v respectively. Its average speed for the complete journey is:
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Question

A particle has to cover a total distance D. It covers the first D/3 with speed v. The remaining distance is covered in two equal time intervals with speeds 2v and 3v respectively. Its average speed for the complete journey is:

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G1 Physics · Accepted Answer

Time for first D/3: t₁ = D/(3v). Let each of the two equal time intervals in the remaining journey be τ. Then 2vτ + 3vτ = 2D/3 ⇒ 5vτ = 2D/3 ⇒ τ = 2D/(15v). Total time = D/(3v) + 2τ = 5D/(15v) + 4D/(15v) = 3D/(5v). Average speed = D / [3D/(5v)] = 5v/3.