Multiple choice

$A$ person goes from point $A$ to point $B$ with speed $V_{1}$ and comes back to point $A$ from point $B$ with speed $V_{2}$. Its average speed and average velocity respectively are

  1. $0,\ 0$
  2. $\dfrac{V_{1}+V_{2}}{2}\ ,\ 0$
  3. $\dfrac{V_{1}+V_{2}}{4}\ ,\ 0$
  4. $\dfrac{2V_{1}V_{2}}{V_{1}+V_{2}}, \ 0$
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D Correct answer
Explanation

Average speed is total distance divided by total time, which for a round trip is 2V1V2 / (V1+V2). Average velocity is displacement divided by time; since the person returns to the starting point, displacement is 0.

AI explanation

Because the person travels equal distances at two different speeds, the average speed is calculated using the harmonic mean formula: 2 times V1 times V2 divided by V1 plus V2. Average velocity is defined as total displacement divided by total time taken. Since the person returns to the starting point A, the total displacement is 0, making the average velocity 0. Therefore, the average speed and average velocity respectively are 2 times V1 times V2 divided by V1 plus V2, and 0.

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