Multiple choice

A particle covers half of its total distance with speed $v_{1}$ and the rest half distance with speed $v_{2}$. Its average speed during the complete journey is :

  1. $\dfrac{v_{1}+v_{2}}{2}$
  2. $\dfrac{v_{1}v_{2}}{v_{1}+v_{2}}$
  3. $\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}$
  4. $\dfrac{v_{1}^{2}v_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance be 2d. Time = d/v1 + d/v2 = d(v1+v2)/(v1*v2). Average speed = 2d / (d(v1+v2)/(v1*v2)) = 2*v1*v2 / (v1+v2).

AI explanation

When equal distances are covered at two different speeds, the average speed is calculated using the harmonic mean formula. The formula for average speed is two multiplied by the product of the two speeds, divided by the sum of the two speeds. Substituting v1 and v2 gives (2*v1*v2) divided by (v1 + v2).

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