Read each statement below carefully and state with reasons and examples, if it is true or false 

A particle in one-dimensional motion

$(a)$ with zero speed at an instant may have non-zero acceleration at that instant

$(b)$ with zero speed may have non-zero velocity.

$(c)$ with constant speed must have zero acceleration.

$(d)$ with positive value of acceleration must be speeding up.

(a) True, when an object is thrown vertically up in the air, its speed becomes zero at maximum height. However, it has acceleration equal to the acceleration due to gravity (g) that acts in the downward direction at that point.

(b) Speed is the magnitude of velocity. When speed is zero, the magnitude of velocity along with the velocity is zero.

(c) Speed is the magnitude of velocity. Constant speed does not imply constant velocity as direction change may happen. Such a scenario is uniform circular motion of a particle about a center. In such a case, acceleration is not zero.

(d) This statement is false in the situation when acceleration is positive and velocity is negative at the instant time taken as origin. Then, for all the time before velocity becomes zero, there is slowing down of the particle. Such a case happens when a particle is projected upwards.

This statement is true when both velocity and acceleration are positive, at the instant time taken as origin. Such a case happens when a particle is moving with positive acceleration or falling vertically downwards from a height.