No, if the path of a particle is a circle with an infinitely large radius, it means that the particle is moving in a straight line, not in a curved path. In this case, the concept of constant velocity still holds, and there is no acceleration.
In circular motion, the acceleration is directed towards the center of the circle and is given by the equation:
a = v^2 / r,
where: a is the acceleration, v is the velocity of the particle, r is the radius of the circular path.
However, when the radius (r) is infinitely large, the acceleration becomes zero because the denominator of the equation approaches infinity. Therefore, in the case of a straight line or a path with an infinitely large radius, the acceleration is zero, and the particle can maintain a constant velocity.
It's important to note that in physics, a straight line can be considered a circle with an infinitely large radius, but it's not accurate to say that there is acceleration due to the radius in this case. Acceleration in circular motion arises from the change in direction, which is absent in a straight line.