can there be motion in two dimensions with an acceleration only in 1 D? show this with eg.

Yes, there can be motion in two dimension with an acceleration only in one dimension.

Example: Consider a ball thrown at an angle with the horizontal. Here, the ball is moving in a 2 dimensional plane. The plane is perpendicular to the horizontal. The horizontal component of the initial velocity of the ball remains constant because there is no force acting on it in the horizontal direction. The vertical component of velocity is changing due to the force of earth's gravity. The acceleration in the vertically downward direction is 'g'. So, we have a 2 dimensional motion with an acceleration only in 1 dimension.