This animation shows an example of circular motion where the linear velocity of the object (v) is steadily increasing.
You can see that as v increases both the centripetal acceleration and the centripetal force also increase. The length of the red arrow represents the magnitude of the both the centripetal force and centripetal acceleration.

The linear velocity of the ball increases to 7.5 ms^{-1}, after which the acceleration in orbit becomes zero and the ball orbits at a constant velocity.