Multiple choice

If a car covers $\dfrac{2}{5^{th}}$ of the total distance with $v_{1}$ speed and $\dfrac{3}{5^{th}}$ distance with $v_{2}$ then average speed:

  1.  $\dfrac{1}{2}\sqrt{v_{1}v_{2}}$
  2. $\dfrac{v_{1}+v_{2}}{2}$
  3.  $\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}$
  4. $\dfrac{5v_{1}v_{2}}{3v_{1}+2v_{2}}$
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D Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance be D. Time t1 = (2D/5) / v1 and t2 = (3D/5) / v2. Total time = (2D/5v1) + (3D/5v2) = (2Dv2 + 3Dv1) / (5v1v2). Average speed = D / [(2Dv2 + 3Dv1) / (5v1v2)] = 5v1v2 / (3v1 + 2v2).

AI explanation

The formula for average speed when distances are covered at different speeds is Total Distance divided by Total Time. Let the total distance be 1, making the total time (2/5) divided by v1 plus (3/5) divided by v2. Simplifying 1 divided by (2/(5*v1) + 3/(5*v2)) gives the average speed as (5*v1*v2) / (3*v1 + 2*v2).

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