State whether the following statements are true or false:
$(a)$ Velocity can change without a change in speed.
$(b)$ The total distance covered by a freely falling body in a given time is directly proportional to the time.
$(c)$ $A$ particle is a point object that possesses dimensions.

(A) True. Velocity is a vector quantity; it can change if the direction of motion changes even if the speed remains constant (e.g.,uniform circular motion).
$(b)$ False. According to the equation of motion $s = ut + \frac{1}{2}at^2$,for a freely falling body $(u=0, a=g)$,the distance $s = \frac{1}{2}gt^2$. Thus,the distance is proportional to the square of the time $(s \propto t^2)$,not the time itself.
$(c)$ False. $A$ particle is defined as a point object that has mass but possesses no dimensions (negligible size).