Multiple choice

A particle travel half of the distance of a straight journey with a speed $6 m/s$. The remaining part of the distance is covered with speed $2 m/s$ for half of the time remaining journey and with speed $4 m/s$ for other half of time. The average speed of the particle is

  1. $3 m/s$
  2. $4 m/s$
  3. $3/4 m/s$
  4. $5 m/s$
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B Correct answer
Explanation

Let total distance be 2D. First half D at 6 m/s takes time t1 = D/6. Remaining distance D is covered in two halves of time t2. Distance covered = 2*t2 + 4*t2 = 6*t2 = D, so t2 = D/6. Total time = D/6 + 2*(D/6) = D/2. Average speed = 2D / (D/2) = 4 m/s.

AI explanation

Let the total distance of the journey be 2x, meaning the first half distance x is covered at 6 m/s, taking a time of x/6 seconds. For the second half distance x, let the time taken be 2t, which gives the equation x = 2t multiplied by (2 + 4)/2, resulting in x = 6t. The total time for the journey is x/6 + 2t, which simplifies to t + 2t = 3t. The average speed is the total distance 2x divided by the total time 3t, which equals 12t divided by 3t, yielding 4 m/s.

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