Explain how an object moving at a constant speed can have a nonzero acceleration

Its very simple if a body is moving in circle the magnitude of its velocity remain constant  but its direction changes because velocity is directed towards tangent and at every point in a cirlce its direction will be different (along tangent) so velocity is not uniform .As acceleration is the rate  change of velocity  so it will be non zero because velocity is changing due to its direction.

Amethod of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.