Velocity

Velocity is the speed of an object plus its direction of travel. Speed measures how fast an object covers distance, and is measured in units such as miles per hour or meters per second. An example of speed is 55 miles per hour, while an example of velocity is 55 miles per hour heading west. In everyday nonscientific contexts, the words “speed” and “velocity” are typically used synonymously, but in physics, the inclusion of direction when measuring velocity is a crucial distinction. Because speed is measured using just the one quantity, it is called a scalar; because velocity refers to the quantity (speed) and direction, it is called a vector.

More specifically, measuring speed takes into account distance—how far an object travels, or how much ground it covers—whereas velocity is concerned with displacement—how far the object moves from its original position. For example, if an object starts from one point and travels in a circle, returning to its starting point, then it traveled at some average speed, perhaps 5 meters per second, but its average velocity was zero, because its displacement was zero—its final location did not change. Similarly, if an object travels in a straight line 4 miles north and then turns left, traveling 3 miles west before stopping, the average speed would be measured based on how far it traveled straight plus how far it traveled to the left (7 miles total); thus, if it took an hour to travel that distance, the average speed was 7 miles per hour. On the other hand, the velocity would be measured based on the straight line from the starting point to the ending point—the hypotenuse of the right triangle created by the two directions of travel (5 miles); thus, the average velocity would be 5 miles per hour northwest.

Background

Since ancient times, velocity has been a key part of developing many basic concepts in physics, such as momentum and kinetic energy.

Momentum was observed as an aspect of objects in motion from the time of ancient Greece. The Greek philosopher Aristotle (ca. 384–ca. 322 BCE) developed the first groundings of a theory of momentum, which was critiqued and reworked some eight centuries later by the Byzantine philosopher John Philoponus (ca. 490–ca. 570 CE). Philoponus called his theory “impetus,” which entails that an object will remain in motion until its energy is exhausted. This view was further developed in the Islamic world by the eleventh-century Persian scholar Avicenna. These ideas would eventually travel back to Europe and reach scientists such as Galileo Galilei, René Descartes, and Isaac Newton in the sixteenth and seventeenth centuries. By the eighteenth century the formal mathematical formulation of momentum was in use, today rendered as p = mv, where p is momentum, m is mass, and v is velocity.

Kinetic energy, or the energy that an object has by virtue of its motion, is defined at one-half its mass times its velocity squared (½mv²). The formulation of kinetic energy was developed in 1829 by the French mathematician Gaspard-Gustave Coriolis (1792–1843). The term kinetic energy was not coined until some twenty years later by the British mathematician William Thomson (1824–1907), later known as Lord Kelvin.

Velocity Today

Velocity is a key concept in the study of physics; an understanding of velocity is fundamental to understanding kinetic energy, momentum, and other concepts on which much of modern engineering and transportation technology is based.

Kinetic energy is the energy of an object in motion. As the velocity and mass of the object increase, so too does the kinetic energy. For example, a roller coaster ride must be designed in such a way as to capitalize on the energy produced from the first hill to power the ride until the roller coaster makes it back to its starting position.

Momentum is the product of mass and velocity. Just as is the case for kinetic energy, as mass and velocity increase, so too does the momentum of an object. The concept of momentum is used in forensic investigations to determine fault and liability in situations such as automobile accidents. It is also used in billiards to determine how hard and where to hit the cue ball in order to make a shot.

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