There are a number of factors that contributed to the relatively swift rise to power of the United States. Here are just a few:
The U.S. is separated from Europe and Asia by two major oceans. This allowed the U.S. to come out of both World War I and World War II relatively unscathed. While the other countries had to spend time and money rebuilding, the U.S. was able to focus on economic growth. 
Additionally, the U.S. had made a substantial amount of money during World War II selling military supplies to its allies. This helped bolster the economy, and put in place countless factories that were able to continue to be used for manufacturing long after the war. 
A Strong Military and a Strong Economy
The growth of the country's own military, along with the fact that they had nuclear weapons made them a military force to be reckoned with. The combination of the strong economy and strong military at a time when most other countries in the world were struggling to rebuild after the war led to the U.S. becoming a major world power. 
Economic and military growth that resulted from war are only one part of the equation, however. There are other factors that helped fuel the rapid economic growth of the United States. For one thing, its tremendous number of ports and inland waterways made it easy and inexpensive to transport goods, allowing for trade with many other countries.
An Abundance of Natural Resources
Another major contributing factor to the rise in power of the United States is its incredible abundance of natural resources. Not only does it produce fossil fuels like coal, natural gas and oil, but it also has rich farmland, plenty of wood for building, metals that can be mined from the ground for trade and countless other natural resources. It produces practically everything it needs to survive without having to rely on other countries. 
The United States is also located in a relatively temperate climate, with weather that is well-suited to agriculture, but cool enough that it does not harbor tropical diseases. Its vast size means that it spans across a number of different growing zones, allowing farmers to grow a tremendous variety of crops.
Other factors that have helped fuel the United States' rise to power include the form of government that the country adopted, the determination and ambition of the immigrants who moved to the U.S. to start a new life, the protection of personal freedoms offered by the Constitution and too many other factors to name.
Here are a couple of videos that help shed more light on America's rise to power: