The point moves along a curvilinear speed with a constant absolute value. does this point have acceleration?

When a material point moves with a constant modulus velocity along a curved trajectory, it has an acceleration. Since acceleration is a vector quantity, it has a certain direction and shows how the speed changes. With a curvilinear motion, the direction of the velocity (it is also a vector quantity) of a material point is always directed tangentially to the trajectory, which means that the direction of the velocity is constantly changing. Acceleration characterizes the change in speed, therefore, the direction of the speed changes, which means there is acceleration.