If the flat Euclidean space around an object suddenly had a linear slope, the object would experience certain effects with respect to an inertial frame. Let's consider the scenario where the slope is constant and aligned in a specific direction.
Constant velocity: Initially, the object would start moving due to the slope. Since the slope is linear and constant, it would provide a continuous force on the object, causing it to accelerate. As long as the force remains constant, the object would continue to accelerate, eventually reaching a constant velocity. This assumes no other forces are acting on the object, such as friction or external forces.
Acceleration: The object would experience a non-zero acceleration due to the linear slope. Initially, the acceleration would be non-zero because the force from the slope would cause the object to gain speed. However, once the object reaches a constant velocity, the net force acting on it becomes zero, resulting in zero acceleration. This assumes there are no other forces acting on the object.
It's important to note that in an inertial frame, an object will only experience a net force if there is an external force acting upon it. In the scenario you described, where the slope is the only force acting on the object, it would eventually achieve a constant velocity without any further acceleration.