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New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and entertainment. The home of the United Nations Headquarters, New York is an important center for international affairs and is widely deemed the cultural capital of the world. The city is also referred to as New York City or the City of New York to distinguish it from the state of New York, of which it is a part.

Located on one of the world's largest natural harbors, New York City consists of five boroughs which were consolidated in 1898: The Bronx, Brooklyn, Manhattan, Queens, and Staten Island. With a 2010 United States Census population of 8,175,133 distributed over a land area of just 305 square miles (790 km²), New York is the most densely populated major city in the United States. As many as 800 languages are spoken in New York, making it the most linguistically diverse city in the world. The New York City Metropolitan Area's population is the United States' largest, estimated at 18.9 million people distributed over 6,720 square miles (17,400 km²), and is also part of the most populous combined statistical area in the United States, containing 22.2 million people as of 2009 Census estimates. New York has the largest internet presence of any location in the world; registering 7.1 billion search results as of December 2011.

In kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero .

Like velocity, speed has the dimensions of a length divided by a time; the SI unit of speed is the meter per second, but the most usual unit of speed in everyday usage is the kilometer per hour or, in the USA and the UK, miles per hour. For air and marine travel the knot is commonly used.

The fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in vacuum c = 299,792,458 meters per second, approximately 1079 million kilometers per hour (671,000,000 mph). Matter cannot quite reach the speed of light, as this would require an infinite amount of energy.

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant direction, typically constrains the object to motion in a straight path. A car moving at a constant 20 kilometers per hour in a circular path does not have a constant velocity. The rate of change in velocity is acceleration. Velocity is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed, a quantity that is measured in metres per second (m/s or ms⁻¹) when using the SI (metric) system.

For example, "5 metres per second" is a scalar and not a vector, whereas "5 metres per second east" is a vector. The average velocity v of an object moving through a displacement during a time interval (Δt) is described by the formula:

The rate of change of velocity is acceleration – how an object's speed or direction of travel changes over time, and how it is changing at a particular point in time.