Multiple choice

A passenger travels along the straight road for half the distance with velocity, ${ v }{ 1 }$ and the remaining half distance with velocity, ${ v }{ 2 }$. Then average velocity is given by

  1. ${ v }_{ 1 }{ v }_{ 2 }$
  2. $\dfrac{v_2^2 }{ v _1^2}$
  3. $\dfrac{{ \left( { v }_{ 1 }+{ v }_{ 2 } \right) }}{2}$
  4. $\dfrac{2{ v }_{ 1 }{ v }_{ 2 }}{{ \left( { v }_{ 1 }+{ v }_{ 2 } \right) }}$
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D Correct answer
Explanation

Average velocity is total displacement divided by total time. If distance is d, total distance is 2d. Time taken is d/v1 + d/v2. Average velocity = 2d / (d/v1 + d/v2) = 2 / (1/v1 + 1/v2) = 2v1v2 / (v1 + v2).

AI explanation

Average velocity is calculated by dividing the total displacement by the total time taken. Let the total distance be 2d, so the time taken for the first half is d divided by v1 and the time for the second half is d divided by v2. The total displacement equals the total distance of 2d since the passenger travels along a straight road, and the total time is d divided by v1 plus d divided by v2, which simplifies to d times the sum of v1 and v2, all divided by v1 times v2. Dividing 2d by this total time and canceling out the distance d, the average velocity is given by 2 times v1 times v2 divided by the sum of v1 and v2.

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