When the space race began the united states realized that

When the space race began the United States realized that the USSR could use rockets to carry nuclear weapons.

Explanation:

The space race was an informal rivalry between the United States and the Soviet Union that lasted from about 1957 to 1975. The superpowers (US and USSR) competed to explore space and get the first artificial satellite and human into space, and then get humans to the moon.  

The background was the tension between the post-World War II superpowers, called Cold War. The race started in reality after the Soviet Union fired Sputnik 1 on October 4, 1957. It became an important part of the Cold War, helping to raise morale and develop new weapon technology.

Both nations distrusted each other, and saw progress in space technology as covert military developments, so that each technological development was in turn almost immediately counteracted by the counterpart. Thus, the Soviet satellite technology was considered by the Americans as a potential missile technology, and in turn the developments in matters of oxygen tubes resistant to space pressure were considered as part of an American amphibious fight project by the Soviets.