Answer
Yes, a set of x- and y-axes can be chosen so that the acceleration of the object has only one non-zero component.
We can choose the x-axis so that the x-axis is parallel to the direction of the net force.
Work Step by Step
Yes, a set of x- and y-axes can be chosen so that the acceleration of the object has only one non-zero component.
Let $F_{net}$ be the net force resulting from the two perpendicular forces. Choose the x-axis so that the x-axis is parallel to the direction of the net force. Then the y-axis would be perpendicular to the direction of the net force.
We know that the acceleration vector must be in the same direction as the net force $F_{net}$. Therefore, the component of the acceleration is zero along the y-axis and non-zero along the x-axis.
