Read each statement below carefully and state with reasons and examples,if it is true or false for 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 upward,its speed becomes zero at the maximum height. However,it still experiences an acceleration equal to the acceleration due to gravity $(g)$ acting downwards.
$(b)$ False. Speed is the magnitude of velocity. If the speed is zero,the magnitude of the velocity is zero,which implies the velocity itself must be zero.
$(c)$ False. Constant speed does not imply constant velocity because the direction of motion can change. For example,in uniform circular motion,the speed is constant,but the velocity changes due to a change in direction,resulting in non-zero centripetal acceleration.
$(d)$ False. If the acceleration is positive but the velocity is negative (e.g.,an object moving in the negative direction while being decelerated by a positive force),the object is slowing down. It only speeds up if the velocity and acceleration have the same sign.