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JEE MainPhysicsMotion in One Dimension

A metro train starts from rest and accelerates uniformly to a maximum speed. It travels at this constant maximum speed for 10 s and then decelerates uniformly to come to a halt. If the total time of travel is 50 s and the total distance covered is 600 m , the maximum speed reached by the train is

Options

  1. A12 m/s
  2. B60 m/s
  3. C24 m/s
  4. D20 m/s

Correct answer

D. 20 m/s

Step-by-step solution

The velocity-time graph of the train's motion forms a trapezium. The parallel sides of the trapezium represent the total time of travel and the time spent at constant speed. Base of trapezium = 50 s Top parallel side = 10 s The height of the trapezium represents the maximum speed, v_ max . The total distance covered is the area under the velocity-time graph. Distance = 1 2 ( Sum of parallel sides ) Height 600 = 1 2 (50 + 10) v_ max 600 = 1 2 60 v_ max 600 = 30 v_ max v_ max = 20 m/s Answer: 20 m/s

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