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The area under the velocity-time graph of a particle is equal to its

  • A.acceleration
  • B.displacement
  • C.speed
  • D.velocity
  • E.angular velocity

Answer: B

The area under a velocity-time graph equals the displacement.

Over a short time dt the displacement is v dt, the area of a thin strip under the graph. Adding all the strips, the total area between the graph and the time axis is the total displacement, with areas below the axis counted as negative.

Acceleration is the slope of the velocity-time graph, not its area. Velocity and speed are the values read off the graph, and angular velocity belongs to rotation. (Distance travelled is the area if parts below the axis are counted as positive.)

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