State which of the following situations are possible and give an example for each of these:
$(a)$ An object with a constant acceleration but with zero velocity.
$(b)$ An object moving with an acceleration but with uniform speed.
$(c)$ An object moving in a certain direction with an acceleration in the perpendicular direction.

(N/A) Possible.
When a ball is thrown vertically upwards,at its maximum height,its velocity is zero,but it still experiences a constant acceleration due to gravity $(g = 9.8\,m/s^2)$ acting downwards.
$(b)$ Possible.
When an object moves in a circular path with a uniform speed,its velocity changes continuously due to the change in direction. This change in velocity results in a centripetal acceleration directed towards the center of the circle.
$(c)$ Possible.
An object moving in a circular path is a classic example. The velocity of the object is tangential to the path,while the centripetal acceleration acts towards the center of the circle,which is perpendicular to the direction of motion.