Acceleration is a VECTOR quantity. That means it corresponds to a specific direction. In two dimensional motion specific direction does not exist (according to graph). Thus this statement is FALSE [my name is meghang. School children's academy. I made my own answer. Am I not intelligent. By the way nice question]
It is possible. velocity and acceleration are two different quantities.
let's say it has velocity in both x an y direction and have acceleration only in x direction. Then its velocity in y direction will be constant and velocity in x direction will be changing.
So, it is possible.