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The velocity (v) - time (t) graph of a particle cuts the time axis, then the particle

  • A.has maximum displacement at that instant
  • B.reverses its direction of motion at that instant
  • C.has a constant velocity throughoutits motion
  • D.has maximum acceleration at that point
  • E.has maximum velocity at that instant

Answer: B

The particle reverses its direction of motion at that instant.

Where the v-t graph cuts the time axis, the velocity is zero and changes sign, from positive to negative or the other way. A change in the sign of velocity is a reversal of the direction of motion, as at the top of a ball's flight.

The displacement there is only a turning point: a maximum if the velocity goes from positive to negative, a minimum if it goes the other way, so 'maximum displacement' is not true in general. The velocity is zero, not maximum, and it is changing, not constant. The graph's crossing says nothing about the acceleration being maximum.

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