## acceleration

**-**

## Acceleration

# Acceleration

An object is said to be accelerating if its velocity is changing, either in direction or magnitude. Acceleration is a vector quantity. If, however, when acceleration is known to be in a straight line, it is often specified as a scalar quantity (pure number). Since the unit of velocity is distance per unit time, the unit of acceleration is velocity per unit time; in metric units, this is (m/s)/s or m/s^{2}.

A material object only accelerates when under the influence of a nonzero net force. Sir Isaac Newton (1642–1727) defined acceleration in his second law of motion as the ratio of a force acting on an object to the mass of the object: *a* = *f/m*.

## History

The study of motion by Galileo Galilei (1564–1642) in the late sixteenth and early seventeenth centuries and by Sir Isaac Newton in the mid-seventeenth century is a cornerstone of modern Western experimental science. For some 20 years, Galileo painstakingly timed the motions of objects rolling down smooth inclines. He discovered that the distance an object traveled was proportional to the square of the time that it was in motion. From these experiments came the first correct concept of accelerated motion.

Newton wanted to know what the character of acceleration was, but also why it occurred at all. In order to produce a model that would help explain how the known universe of the seventeenth century worked, Newton gave science and physics a rigorously defined concept of “force.” In his second law of motion, he stated that acceleration is caused by an unbalanced force (such as a push or a pull) acting on an object. Newton showed that gravity could be considered a special type of acceleration. The acceleration of a mass by gravity produces the force we call weight. A general definition of mass is that it is the quantity of matter in a body; weight, on the other hand, is the force experienced by a stationary body in a given gravitational field. The mass of a body does not, in Newtonian (non-relativistic) physics, vary depending on its location or state of motion; its weight does.

## Linear acceleration

An object that is moving in a straight line is accelerating if its velocity (commonly referred to as its speed) is increasing or decreasing. Straight-line acceleration (*a* ) can be either positive or negative, depending on whether its direction is positive (*a* ) or negative (*a* ).

An automobile’s motion can help explain linear acceleration. The car’s speedometer measures velocity magnitude. If the car starts from rest and accelerates steadily in a positive direction to 60 miles per hour (mph) in 10 seconds, what is its acceleration throughout those 10 seconds? The car’s velocity changes 60 mph in 10 seconds, so its acceleration is 60 mph/10 s = + 6 mi/hr/s. (These units could be converted into m/s^{2} if necessary.) That means its acceleration changes six miles per hour for each second it accelerates. If the car started at 60 mph and stopped after 10 seconds of steady braking, its average acceleration would be equal to –6 mi/hr/s.

## Curvilinear acceleration

In curvilinear motion—motion along any path other than a straight line—an object’s magnitude of velocity may or may not remain constant but the direction of its motion changes constantly. It is therefore being accelerated. If our automobile is going at a constant 60 mph around a bend in the road, it undergoes acceleration because its direction is changing while it is on the curve. Roller coasters and other amusement park rides cause their riders to experience rapid changes in acceleration by making them move rapidly along curved paths.

## G forces

The force experienced by an object due to acceleration is sometimes expressed as a fraction of the

### KEY TERMS

**Acceleration—** The rate at which the velocity of an object changes over time.

**Circular acceleration—** Acceleration in which the direction of motion is changing.

**Force—** Influence exerted on an object by an outside agent that produces an acceleration changing the object’s state of motion.

**“G” forces—** The apparent increase in body weight due to rapid acceleration; a force of 2 Gs means that a body feels a force of twice its body weight acting on it.

**Gravity—** The special acceleration of 9.81 m/s^{2}exerted by the attraction of the mass of Earth on nearby objects at Earth’s surface.

**Linear acceleration—** Acceleration in which the magnitude (velocity) of the motion is changing.

**Mass—** A measure of the quantity of matter in an object.

**Vector—** A quantity or term that can be expressed in terms of both magnitude (a number) and a direction.

**Velocity—** The speed and direction of a moving object.

**Weightlessness—** A condition caused by accelerating freely toward Earth at the same rate as gravity and not feeling the usual effects of weight.

force the same object would experience due to its own weight if stationary at the surface of Earth, referenced as 1 G. An acceleration that makes an object feel a force equal to twice its weight, for example, subjects it to 2 Gs. Astronauts experience as much as 7 Gs during lift-off of a space shuttle, but once in free-falling orbit they experience no G force. The concept of “weightlessness” in space is often misunderstood. It is not caused by the fact that objects in low Earth orbit are far from Earth’s mass; they are, in fact, subject to almost as much gravity as objects at the surface. They are, however, falling freely under the influence of gravity, like people in a falling elevator. They remain aloft because of their tangential or sideways motion. In a sense they are always falling freely toward Earth, but moving sideways fast enough to miss it. If an orbiting object’s sideways velocity is decreased, say by firing a rocket against its direction of motion, it falls toward the surface of Earth.

*See also* Accelerators; Gravity and gravitation; Laws of motion; Velocity.

## Resources

### BOOKS

Bedford, Anthony M., and Wallace Fowler. *Engineering Mechanics: Statics and Dynamics*. Upper Saddle River, NJ: Prentice Hall, 2004.

Burnett, Betty. *The Laws of Motion: Understanding Uniform and Accelerated Motion*. New York: Rosen Publishing Group, 2004.

Milliken, William F. *Equations of Motion*. Cambridge, MA: Bentley Publishers, 2006.

Serway, Raymond A., and Jerry S. Faughn. *College Physics Vol. I*. Belmont, CA: Brooks Cole, 2005.

Touger, Jerold. *Introductory Physics: Building Understanding*. New York: John Wiley & Sons, 2006.

### OTHER

*National Aeronautics and Space Administration*. “Newton’s Laws of Motion.” March 16, 2006. <http://www.lerc.nasa.gov/WWW/K-12/airplane/newton.html> (accessed Oct. 1, 2006).

Kenneth L. Frazier

## Acceleration

# Acceleration

The term acceleration, used in **physics** , is a vector quantity. This means that acceleration contains both a number (its magnitude) and a specific direction. An object is said to be accelerating if its **rate** of change of **velocity** is increasing or decreasing over a period of **time** and/or if its direction of **motion** is changing. The units for acceleration include a **distance** unit and two time units. Examples are m/s2 and mi/hr/s. Sir Isaac Newton (1642-1727) in his second law of motion defined acceleration as the **ratio** of an unbalanced **force** acting on an object to the **mass** of the object.

## History

The study of motion by Galileo Galilei (1564-1642) in the late sixteenth and early seventeenth centuries and by Sir Isaac Newton in the mid-seventeenth century was one of the major cornerstones of modern Western experimental science. Over a period of 20 years, Galileo observed the motions of objects rolling down various inclines and attempted to time these events. He discovered that the distance an object traveled was proportional to the square of the time that it was in motion. From these experiments came the first correct concept of accelerated motion. Newton wanted to know why acceleration occurred. In order to produce a model that would help explain how the known universe of the seventeenth century worked, Newton had to give to science and physics the concept of a force which was mostly unknown at that time. With his second law of motion, he clearly demonstrated that acceleration is caused by an unbalanced force (commonly called a push or a pull) acting on an object. What we call gravity, Newton showed was nothing more than a special type of acceleration. The interaction of the acceleration of gravity on the mass of our body produces the force which is called weight. A general definition of mass is that it refers to the quantity of **matter** in a body.

## Linear acceleration

An object that is moving in a straight line is accelerating if its velocity (sometimes incorrectly referred to as speed) is increasing or decreasing during a given period of time. Acceleration (a) can be either positive or **negative** depending on whether the velocity is increasing (+a) or decreasing (-a). An automobile's motion can help explain linear acceleration. The speedometer measures the velocity. If the auto starts from rest and accelerates to 60 MPH in 10 seconds, what is the acceleration? The auto's velocity changed 60 MPH in 10 seconds. Therefore, its acceleration is 60 MPH/10 s = +6 mi/hr/s. That means its acceleration changed six miles per hour every second it was moving. Notice there are one distance unit and two time units in the answer. If the auto had started at 60 MPH and then stopped in 10 seconds after the brakes were applied, the acceleration would be = -6 mi/hr/s. If this **automobile** changes direction while moving at this constant acceleration, it will have a different acceleration because the new vector will be different from the original vector. The **mathematics** of vectors is quite complex.

## Circular acceleration

In circular motion, the velocity may remain constant but the direction of motion will change. If our automobile is going down the road at a constant 60 MPH and it goes around a **curve** in the road, the auto undergoes acceleration because its direction is constantly changing while it is in the curve. Roller coasters and other amusement park rides produce rapid changes in acceleration (sometimes called centripetal acceleration) which will cause such effects as "g" forces, "weightlessness" and other real or imaginary forces to act on the body, causing dramatic experiences to occur. Astronauts experience as much as 7 "gs" during lift-off of the **space shuttle** but once in **orbit** it appears that they have lost all their weight. The concept of "weightlessness" in **space** is a highly misunderstood phenomena. It is not caused by the fact that the shuttle is so far from the **Earth** ; it is produced because the space shuttle is in free fall under the influence of gravity. The shuttle is traveling 17,400 MPH around Earth and it is continually falling toward Earth, but the Earth falls away from the shuttle at exactly the same rate.

## Force and acceleration

Before the time of Sir Isaac Newton, the concept of force was unknown. Newton's second law was a simple equation and an insight that significantly affected physics in the seventeenth century as well as today. In the second law, given any object of mass (m), the acceleration (a) given to that object is directly proportional to the net force (F) acting on the object and inversely proportional to the mass of the object. Symbolically, this means a = F/m or in its more familiar form F = ma. In order for acceleration to occur, a net force must act on an object.

See also Accelerators; Gravity and gravitation; Laws of motion; Velocity.

## Resources

### books

Cohen, I. Bernard. *Introduction to Newton's Principia.* Lincoln, NE: iUniverse, 1999.

Galilei, Galileo. *Dialogues Concerning Two New Sciences.* Translated by H. Crew and A. DiSalvo. Glendale, CA: Prometheus Books, 1991.

Goldstein, Herbert, Charles P. Poole, and John L. Safko. *Classical Mechanics.* 3rd ed. New York, Prentice Hall, 2002.

Hewitt, Paul. *Conceptual Physics.* Englewood Cliffs, NJ: Prentice Hall, 2001.

Meriam, J.L., and L.G. Kraige. *Engineering Mechanics, Dynamics.* 5th ed. New York: John Wiley & Sons, 2002.

*Methods of Motion: An Introduction to Mechanics.* Washington, DC: National Science Teachers Association, 1992.

Serway, Raymond, Jerry S. Faughn, and Clement J. Moses. *College Physics.* 6th ed. Pacific Grove, CA: Brooks/Cole, 2002.

Kenneth L. Frazier

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .**Acceleration**—The rate at which the velocity of an object changes over time.

**Circular acceleration**—Acceleration in which the direction of motion is changing.

**Force**—Influence exerted on an object by an outside agent which produces an acceleration changing the object's state of motion.

**"G" forces**—The apparent increase in body weight due to rapid acceleration; a force of 2 "G"s means that a body feels a force of twice its body weight acting on it.

**Gravity**—The special acceleration of 9.81 m/s2 exerted by the attraction of the mass of the Earth on nearby objects at Earth's surface.

**Linear acceleration**—Acceleration in which the magnitude (velocity) of the motion is changing.

**Mass**—A measure of the quantity of matter in an object.

**Vector**—A quantity or term that can be expressed in terms of both magnitude (a number) and a direction.

**Velocity**—The speed and direction of a moving object.

**Weightlessness**—A condition caused by accelerating freely toward the Earth at the same rate as gravity and not feeling the usual effects of weight.

## Acceleration

# Acceleration

Acceleration is a measure of the rate at which the velocity of an object is changing. If you are riding in a car traveling in a straight line at a constant 50 kilometers per hour, you experience no acceleration because the car's velocity (rate of motion) is not changing. If the car begins to speed up, acceleration occurs because the car's velocity increases. If the car slows down, negative acceleration, or deceleration, occurs because the car's velocity decreases.

## Acceleration and force

Our understanding of acceleration is due to the work of two great scientists, Italian physicist Galileo Galilei (1564–1642) and English physicist Isaac Newton (1642–1727). During the late sixteenth and early seventeenth centuries, Galileo first observed the motion of objects rolling down an inclined plane. He wrote mathematical equations that showed how the velocities of these objects increased as they rolled down the planes. These equations first described the idea of accelerated motion.

Some years later, Newton explained the observations made by Galileo. He said that the velocity of an object changes only when a force acts on that object. In the case of a ball rolling down a plane, that force is the force of gravity. Newton's discovery of the relationship between force and acceleration became one of the fundamental concepts in modern physics.

## Linear acceleration

An object moving in a straight line is accelerated only if a force acts on it. For example, imagine a ball rolling across a smooth flat surface with a velocity of 5 meters per second. Then suppose someone hits the ball lightly with a bat. The additional force on the ball provided by the bat will cause the ball to move faster.

Suppose that the ball's new velocity is 10 meters per second and that it takes 2 seconds to accelerate from its original velocity (5 meters per second) to its new velocity (10 meters per second). The acceleration of the ball, then, is the change in velocity of 5 meters per second (10 meters per second minus 5 meters per second) divided by the time it takes to increase in velocity (2 seconds), or 5 meters per second divided by 2 seconds. The acceleration is 2.5 meters per second per second. The unit of measurement used for acceleration—meters per second per second—may sound strange, but it tells by how much the velocity (meters per second) changes in each unit of time (per second).

## Circular acceleration

The acceleration of an object depends on two factors, velocity and direction. An object that moves with constant speed but that changes direction is also accelerating. A car traveling around a curve in the road is accelerating even though its speed remains constant.

## Words to Know

**Acceleration:** The rate at which the velocity and/or direction of an object is changing with respect to time.

**Circular acceleration:** Acceleration in which the direction of motion is changing.

**Force:** A push or pull on an object that will accelerate an object.

**Gravity:** The special acceleration of 9.81 meters per second per second exerted by the attraction of the mass of Earth on nearby objects.

**Linear acceleration:** Acceleration in which the speed of an object is changing.

**Velocity:** The rate at which the position of an object changes with time, including both the speed and the direction.

Another example of circular acceleration is the motion of the Moon around Earth. The Moon travels at a constant speed in its orbit. But it also falls constantly towards Earth's surface. The force of Earth's gravity acts on the Moon not to change its speed but to change the direction in which it is traveling. Again, acceleration occurs when a force acts on an object.

[*See also* **Gravity and gravitation; Laws of motion; Particle accelerators** ]

## acceleration

acceleration, change in the velocity of a body with respect to time. Since velocity is a vector quantity, involving both magnitude and direction, acceleration is also a vector. In order to produce an acceleration, a force must be applied to the body. The magnitude of the force *F* must be directly proportional to both the mass of the body *m* and the desired acceleration *a,* according to Newton's second law of motion, *F*=*ma.* The exact nature of the acceleration produced depends on the relative directions of the original velocity and the force. A force acting in the same direction as the velocity changes only the speed of the body. An appropriate force acting always at right angles to the velocity changes the direction of the velocity but not the speed. An example of such an accelerating force is the gravitational force exerted by a planet on a satellite moving in a circular orbit. A force may also act in the opposite direction from the original velocity. In this case the speed of the body is decreased. Such an acceleration is often referred to as a deceleration. If the acceleration is constant, as for a body falling near the earth, the following formulas may be used to compute the acceleration *a* of a body from knowledge of the elapsed time *t,* the distance *s* through which the body moves in that time, the initial velocity *v*_{i}, and the final velocity *v*_{f}:

a=(v_{f}^{2}-v_{i}^{2})/2sa=2(s-v_{i}t)/t^{2}a=(v_{f}-v_{i})/t

## acceleration

**acceleration** Amount by which the velocity (speed in a particular direction) of an object increases in a certain time.

Acceleration can involve a change in speed and direction. It is measured in metres or feet per second per second (m/s^{2} or ft/s^{2}). For example, if an object accelerates from 20m/s^{2} to 30m/s^{2}, it has accelerated by 10m/s^{2}. A stone dropped over a cliff accelerates from zero velocity at a rate of 9.81m (32.2ft) per second per second, this acceleration being due to the pull of Earth's gravity. The rate of acceleration can be found by applying the equation: acceleration = (change in velocity)/(time taken for change). Deceleration is a decrease in velocity. See also gravitation

## acceleration

**acceleration** A form of heterochrony in which, during the course of evolution, the rate of development of an organism is speeded up and new stages are added to the end of the ancestral developmental sequence without prolonging the total development time. The morphological outcome is an example of peramorphosis, and the developmental sequence (ontogeny) conforms to the theory of recapitulation.

## acceleration

**acceleration** Evolution that occurs by increasing the rate of ontogenetic (see ONTOGENY) development, so that further stages can be added before growth is completed. This form of heterochrony was proposed by E. H. Haeckel as one of the principal modes of evolution.

## acceleration

**acceleration** Evolution that occurs by increasing the rate of ontogenetic (see ontogeny) development, so that further stages can be added before growth is completed. This form of heterochrony was proposed by E. H.Haeckel as one of the principal modes of evolution.

## acceleration

ac·cel·er·a·tion / akˌseləˈrāshən/ • n. increase in the rate or speed of something. ∎ Physics the rate of change of velocity per unit of time. ∎ a vehicle's capacity to gain speed within a short time.

## Acceleration

# ACCELERATION

*A hastening; a shortening of the time until some event takes place.*

A person who has the right to take possession of property at some future time may have that right accelerated if the present holder loses his or her legal right to the property. If a life estate fails for any reason, the remainder is accelerated.

The principle of acceleration can be applied when it becomes clear that one party to a contract is not going to perform his or her obligations. anticipatory repudiation, or the possibility of future breach, makes it possible to

move the right to remedies back to the time of repudiation rather than to wait for the time when performance would be due and an actual breach would occur.