Which one of the following statements is not correct?

Which one of the following statements is not correct?

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If the velocity and acceleration have opposite sign, the object is slowing down

If the velocity is zero at an instant, the acceleration should also be zero at that instant

If the velocity is zero for a time interval; the acceleration is zero at any instant within the time interval

If the position and velocity have opposite sign, the object is moving towards the origin

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC NDA-2 – 2015

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Statement B is not correct. If the velocity of an object is zero at a particular instant, its acceleration at that instant does not necessarily have to be zero. A classic example is an object thrown vertically upwards: at the peak of its trajectory, its instantaneous velocity is zero, but the acceleration due to gravity is still acting on it and is non-zero (approximately 9.8 m/s² downwards).

Acceleration is the rate of change of velocity. Zero velocity at an instant only means the object is momentarily stopped; it does not imply that the velocity is not changing at that instant.

Statement A is correct: if velocity and acceleration have opposite signs, the object is slowing down (e.g., positive velocity, negative acceleration). Statement C is correct: if velocity is zero for a time interval, the object is stationary, meaning its velocity is constant (zero), and thus its acceleration is zero. Statement D is correct: if position and velocity have opposite signs (e.g., positive position, negative velocity means moving towards origin from the positive side; negative position, positive velocity means moving towards origin from the negative side), the object is moving towards the origin (assuming origin is at position=0).

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