If an object is moving along a circular path with an infinitely large radius, it means that the path becomes a straight line. In this case, if the object maintains a constant speed along that straight line, it can be said to have a constant velocity.
Velocity is a vector quantity that includes both magnitude (speed) and direction. So, for an object to have constant velocity, it must maintain a constant speed and move in a straight line. In the scenario you described, the object would satisfy these conditions because the circular path with an infinitely large radius becomes effectively a straight line.
Regarding acceleration, it's important to note that acceleration is a change in velocity, either in terms of magnitude, direction, or both. In circular motion, even if an object has a constant speed along the circular path, its direction is continuously changing. As a result, the object experiences a centripetal acceleration directed toward the center of the circle.
The magnitude of centripetal acceleration is given by the equation a = v^2/r, where "a" represents acceleration, "v" represents the magnitude of velocity (speed), and "r" represents the radius of the circular path. In the case of an infinitely large radius, the centripetal acceleration would be zero, meaning there is no acceleration.
So, if an object is moving along a path that is part of a circle with an infinitely large radius, it can have constant velocity, but there would be no acceleration associated with that motion.