A horse rider covers half the distance with 5 m / s speed. The remaining part of the distance was travelled with speed 10 m / s for half the time and with speed 15 m / s for other half of the time. The mean speed of the rider averaged over the whole time of motion is x/7 m / s. The value of x is ___________.

Solution

Physics sir · 3 steps

Average speed is total distance over total time, so find the time for each half and add them up.

1. First half. Let the total distance be 2d. The first half, d, is covered at 5 m s⁻¹, so it takes d/5.
2. Second half. Let each half of the remaining time be t. The distance covered is 10t + 15t = 25t, and this must equal d. So t = d/25, and the second half takes 2t = 2d/25.

   v_(avg) = 2d/(d/5 + 2d/25) = 2d/(7d/25) = 50/7 m s⁻¹

3. So. The mean speed is 50/7 m s⁻¹, so x = 50.

The common slip: 61.25. Taking the plain average of 5 and 12.5 m s⁻¹ gives 8.75 m s⁻¹, so x = 61.25, not 50. The two halves are equal distances, not equal times.

The idea to keep. Equal times means you may average the speeds directly. Equal distances means you may not. When in doubt, work out total distance and total time.

Answer from the NTA final answer key. Solution by PrepWiser.