Article I, Section 8 Clause 18. Commonly called the 'elastic clause' in the Constitution, it grants Congress the power to do whatever they have to do to carry out the other express powers given to them. What the Congress has to do changes over time, and the courts tell us if they are still meeting the principle of the Elastic Clause, or whether it has overstepped its bounds.
Article V gives spells out how Congress and the states can change the Constitution if it really needs it.
The 10th Amendment allows states to resolve all matters and have all jurisdictions and authorities, unless it is a power expressly given to the federal government. This allows states to change at their own pace, slowly or quickly, as long as the change does not violate Constitutional law. This is why we get such different laws with regards to drinking, traffic laws, etc.
I think that one of the fundamental goals of the Constitution helps to explain why change and adaptation might be embedded within it. The goal of "forming a more perfect union" is a goal that argues at its core that democracy is an experiment and the Constitution's commitment to it is a reflection of how it needs to be adapted and changed, to a certain extent, in order to "get it right." This particular goal and the elements within it help to explore the idea that the Constitution is a document that understands that change within a paradigm is the best way to adapt to the needs of an ever changing society. The Ninth Amendment speaks to this as the framers understood "unenumerated rights" as conceiving entitlements that might have lay outside the grasp of the framers. The inclusion of the 13th, 14th, and 15th Amendments help to bring to light that the document is meant to reflect changing times, and that it should not be static, but rather dynamic. This is the same with later amendments that brought more people into the democratic experience and experiment, such as the 19th and the 26th. The fact that the document outlines how items can be amended to the Constitution also demonstrates a specific feature that allows for change and adaptation. It is the genius of the framers to understand that the Constitution is meant to be the foundation for American legal and political society, but is one that is allowed to reflect its times. This is why the document has changed and has undergone revision without it ever being absent from what we know as the United States of America.