Essay:

after september 2, 1949 both united states and the soviet union had atomic weapons that they could use in the war against each other, in a paragraph analyze how this fact shaped the progress of the cold war and the relationship between two countries and in your response you may want to include the following terms arms race, mutually assured distraction, massive retaliation, and brinkmanship

In the Cold War, the United States (USA) and the Union of Soviet Socialist Republics (USSR) were at odds with each other because of strongly different worldviews.  The USA was committed to capitalism and democratic institutions of government, whereas the USSR was committed to communism and imposed authoritarian government.  Initially, the USA had atomic weapons and the USSR did not.  (The US would not share that technology with the Soviets, who had been their ally in World War II.)  But once the Soviets developed their own atomic weaponry, this led to a massive arms race between the superpowers.  The two nations kept escalating their weapons capabilities and stockpiles.  It got to the point that if the two sides did plunge into war, they would face mutually assured destruction.  John Foster Dulles, the Secretary of State under President Eisenhower, wanted a change from what had been the "containment policy" which the US had followed during the Truman Administration, as recommended then by American diplomat George F. Kennan.   Dulles felt the containment approach put the United States in a weak position, because it only was reactive, trying to contain  communist aggression when it occurred.  Dulles sought to push America's policy in a more active direction; some have labeled his approach "brinkmanship."  In an article in LIFE magazine in 1956, Dulles said, "The ability to get to the verge without getting into the war is the necessary art."  He wasn't afraid to threaten massive retaliation against communist enemy countries as a way of intimidating them.

Eventually (after decades of the arms race and tensions) the US and USSR would pursue policies of detente, which included pledges to reduce their nuclear arsenals.  The arms race and solving the arms race were constant issues affecting the Cold War.