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To accelerate an object is to change its velocity over a period of time. In this strict scientific sense, acceleration can have positive and negative values—respectively called acceleration and deceleration (or retardation) in common speech—as well as change of direction. Acceleration is defined technically as "the rate of change of velocity of an object with respect to time" and is given by the equation
where
a is the acceleration vector
v is the velocity vector expressed in m/s
t is time expressed in seconds.
This equation gives a the units of m/(s·s), or m/s² (read as "metres per second per second", or "metres per second squared").
An alternative equation is:
where
is the average acceleration (m/s²) is the initial velocity (m/s) is the final velocity (m/s) is the time interval (s) Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion. For this centripetal acceleration we haveOne common unit of acceleration is g, one g being the acceleration caused by the gravity of Earth at sea level at 45° latitude (Paris), or about 9.81 m/s².
In classical mechanicsClassical mechanics is a model of the physics of forces acting upon bodies. It is often referred to as Newtonian mechanics after Newton and his laws of motion. Classical mechanics is subdivided into statics (which models objects at rest), kinematics (whic, acceleration is related to force and massMass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. It is a central concept of classical mechanics and related subjects. Strictly speaking, there are two different quantities called mass Inertial mass (assumed to be constant) by way of Newton's second lawNewton's laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. These laws are fundamental to classical mechanics. Newton first published these laws in Philosophiae Naturalis Principia Mathema:
As a result of its invariance under the Galilean transformations, acceleration is an absolute quantity in classical mechanicsClassical mechanics is a model of the physics of forces acting upon bodies. It is often referred to as Newtonian mechanics after Newton and his laws of motion. Classical mechanics is subdivided into statics (which models objects at rest), kinematics (whic.
After defining his theory of special relativitySpecial relativity (SR or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. It replaced Newtonian notions of space and time, and incorporated electromagnetism as represented by Maxwell's equations. The theory is, Albert EinsteinAlbert Einstein ( March 14 1879 April 18 1955) was a theoretical physicist who is widely regarded as the greatest scientist of the 20th century. He proposed the theory of relativity and also made major contributions to the development of quantum mechanics realized that forces felt by objects undergoing constant acceleration are indistinguishable from those in a gravitational field, and thus defined general relativity (which also resolved how gravity's effects could be limited by the speed of light, but that is another story).
A key point of general relativity is that it solved the "why does only one object feel accelerated?" problem which had plagued philosophers and scientists since Newton's time (and caused Newton to endorse absolute space). Simply put, if you hop in your car and accelerate away from your friend, you could say (given your frame of reference) that it is your friend who is accelerating away from you, although only you feel any force. This is also the basis for the popular Twin paradox, which asks why only one twin ages when moving away from his sibling at near light-speed and then returning, since the aging twin can say that it is the other twin that was moving.
In special relativity, only inertial frames of reference (non-accelerated frames) can be used and are equivalent; general relativity considers all frames, even accelerated ones, to be equivalent. With changing velocity, accelerated objects exist in warped space (as do those that reside in a gravitational field). Therefore, frames of reference must include a description of their local spacetime curvature to qualify as complete.
The rate of change of acceleration is known as jerk or jolt.
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