No, it is not possible to have constant velocity and non-zero acceleration. In classical mechanics, acceleration is defined as the rate of change of velocity with respect to time. If the velocity of an object remains constant, it means there is no change in its speed or direction. Therefore, if the velocity is constant, the acceleration must be zero.
Mathematically, if an object has a constant velocity v, its acceleration a can be described as:
a = Δv / Δt
Where Δv is the change in velocity and Δt is the corresponding time interval. If Δv is zero, which is the case for an object with constant velocity, the acceleration a will be zero.
Acceleration represents the rate at which velocity changes. If an object's velocity is not changing, there is no acceleration acting on it. Conversely, if an object has non-zero acceleration, it means its velocity is changing, either in magnitude or direction or both.