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An object moves with speed v₁, v₂ and v₃ along a line segment AB, BC and CD respectively as shown in the figure, where AB = BC and AD = 3AB. Then the average speed of the object will be

Asked in JEE Main 1st Feb 1st Shift 2023 · Distance and average speed

• (1) (v₁ + v₂ + v₃)/3
• (2) (3v₁v₂v₃)/(v₁v₂ + v₂v₃ + v₃v₁)
• (3) (v₁ + v₂ + v₃)/(3v₁v₂v₃)
• (4) (v₁v₂v₃)/(3(v₁v₂ + v₂v₃ + v₃v₁))

Step-by-step solution

Why the other options are wrong

• (1) Arithmetic mean of the three speeds, which needs equal times, not equal distances.
• (3) Inverts the harmonic structure; the expression does not even have the dimensions of speed.
• (4) Puts the 3 in the denominator: divides by 3 instead of multiplying by the total distance 3d.

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