Multiple choice

Two trains start a distance of $2000m$ apart. Train one is moving with a constant speed of $30 m/s$ directly towards train $2$ which starts from rest and accelerates with a constant acceleration of $5m/s^2$ directly towards train 1. When do the trains meet?

  1. $22.9 s$
  2. $34.9 s$
  3. $30 s$
  4. $40 s$
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A Correct answer
Explanation

Relative acceleration = 5 m/s^2. Initial relative velocity = 30 m/s. Distance = 2000 m. Using s = ut + 0.5at^2: 2000 = 30t + 0.5(5)t^2. 2.5t^2 + 30t - 2000 = 0. t^2 + 12t - 800 = 0. Using quadratic formula: t = (-12 + sqrt(144 + 3200)) / 2 = (-12 + 57.8) / 2 = 22.9 s.

AI explanation

Using the equation of motion for uniformly accelerated movement, the sum of the distances covered by both trains equals the initial separation of 2000 m. Train one covers a distance of 30t, while train two covers a distance of 0.5 times 5 times t squared. Setting their sum equal to 2000 gives the quadratic equation 2.5t squared plus 30t minus 2000 equals 0. Using the quadratic formula to solve for the positive root yields a time of approximately 22.9 s. The result is 22.9 s.

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