Multiple choice

Two trains one of length $100\ m$ and another of length $125m$, are moving in mutually opposite directions along parallel lines, meet each other, each with speed $10m/s$. If their acceleration are $0.3m/{s}^{2}$ and $0.2m/{s}^{2}$ respectively, then the time they take to pass each other will be

  1. $5\ s$
  2. $10\ s$
  3. $15\ s$
  4. $20\ s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative initial velocity = 10 - (-10) = 20 m/s. Relative acceleration = 0.3 - (-0.2) = 0.5 m/s^2. Total distance to cover = 100 + 125 = 225 m. Using s = ut + 0.5at^2: 225 = 20t + 0.5(0.5)t^2. 0.25t^2 + 20t - 225 = 0. t^2 + 80t - 900 = 0. (t + 90)(t - 10) = 0. t = 10.

AI explanation

The total relative distance the trains must cover to pass each other is the sum of their lengths, 100 m + 125 m = 225 m. Their relative initial speed is 10 m/s + 10 m/s = 20 m/s, and since they are moving in opposite directions, their relative acceleration is 0.3 + 0.2 = 0.5 m/s^2. Applying the kinematic equation s = ut + (1/2)at^2 yields 225 = 20t + (1/2)(0.5)t^2, which simplifies to t^2 + 80t - 900 = 0. Factoring this quadratic equation gives (t + 90)(t - 10) = 0, so the time taken is 10 s.

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