csatmedium

Consider the following Velocity-Time graph. It shows two trains starting simultaneously on parallel tracks. With reference to the above graph, which one of the following statements is not correct?

  1. A.Train B has an initial acceleration greater than that of Train A.
  2. B.Train B is faster than Train A at all times.
  3. C.Both trains have the same velocity at time t0.
  4. D.Both trains travel the same distance in time t0 units.
▶ Answer & Explanation

Correct answer: B. Train B is faster than Train A at all times.

The velocity-time graph plots velocity on the y-axis and time on the x-axis. Acceleration is represented by the slope of the graph. Train B's graph starts with a steeper slope than Train A's, indicating higher initial acceleration. At time t0, both graphs intersect at the same velocity, meaning both trains have equal velocity at that instant. The area under the velocity-time graph represents the distance traveled. Up to time t0, the area under Train B's curve is greater than that under Train A's curve, indicating Train B travels a greater distance. Therefore, the statement that Train B is faster than Train A at all times is incorrect because their velocities are equal at time t0, and before t0, Train A's velocity is greater.

Source: UPSC csat 2011

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