Question

Select incorrect statement(s).
(A) Zero acceleration of a particle does not necessarily mean that its velocity is zero
(B) Negative acceleration of a particle does not necessarily mean that speed of the particle is decreasing
(C) Zero velocity of a particle does not necessarily mean that its acceleration is zero
(D) If the speed of a particle is constant, its acceleration must be zero

Answer 1

Hint: In this solution, we will use the principles of uniform motion and accelerated motion. We will go through each option individually to select the incorrect statements.

Complete step by step answer:
In option (A), a particle can have zero acceleration but still have non-zero velocity. This is the case in a uniform motion where the object is moving with constant velocity. Acceleration implies that there is a non-zero change in velocity with respect to time so if the velocity is constant but non-zero, the particle can have zero acceleration. Hence option (A) is correct.
In option (B), negative acceleration necessarily implies that the speed of the particle is decreasing. So, option (B) is incorrect.
In option (C), zero velocity does not imply that the acceleration is zero. For e.g., when a ball is released from a height, its velocity will be zero but the acceleration exerted due to gravity will be non-zero so option (C) is correct.
In option (D), constant speed does not imply that acceleration is zero. For e.g., in a circular motion, the speed of the object is constant but the velocity is non-zero because of the change in direction of the object. This implies that the acceleration of the object is non zero since the velocity of the object changes with time, even if the speed is constant.

Hence option (D) is incorrect.

Note: We must not confuse between speed and velocity. Speed is a scalar quantity and has the only magnitude while velocity is a vector quantity and has a direction associated with it too. The magnitude of the velocity vector is equal to the speed of the object.