Cite an example of something that undergoes acceleration while moving at constant speed. Can you also give an example of something that accelerates while traveling at constant velocity? Explain.

when an object is moving in a circle with constant speed but its velocity is constantly changing giving rise to acceleration.

As velocity is vector quantity so a slight change in direction gives acceleration, though the magnitude of velocity and speed may be equal.

Constant velocity cannot give acceleration therefore second statement is not possible.