# Difference between revisions of "Acceleration"

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− | Acceleration, the second [[derivative]] of [[displacement]], is defined to be the change of [[velocity]]. | + | ==Definition== |

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+ | '''Acceleration''', the second [[derivative]] of [[displacement]], is defined to be the change of [[velocity]] per unit time at a certain instance. | ||

A common misconception is that acceleration implies a POSITIVE change of velocity, while it could also mean a NEGATIVE one. | A common misconception is that acceleration implies a POSITIVE change of velocity, while it could also mean a NEGATIVE one. | ||

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+ | ==Formula for Acceleration== | ||

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+ | Let <math>\textbf{v}_1</math> be the velocity of an object at a time <math>t_1</math> and <math>\textbf{v}_2</math> be the velocity of the same object at a time <math>t_2</math>. If acceleration, <math>\textbf{a}</math>, is known to be constant, then <cmath>\textbf{a} = \frac{\textbf{v}_2 -\textbf{v}_1 }{t_2 - t_1}</cmath> Note that velocity is a vector, so the magnitudes cannot be just subtracted in general. | ||

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+ | If acceleration is not constant, then we can treat velocity as a function of time, <math>v(t)</math>. Then, at a particular instance, <cmath>\textbf{a} = \lim_{h\to 0} \frac{v(t+h)-v(t)}{(t+h)-t} = v'(t)</cmath> | ||

[[Category:Physics]] | [[Category:Physics]] |

## Revision as of 13:12, 24 April 2009

## Definition

**Acceleration**, the second derivative of displacement, is defined to be the change of velocity per unit time at a certain instance.

A common misconception is that acceleration implies a POSITIVE change of velocity, while it could also mean a NEGATIVE one.

## Formula for Acceleration

Let be the velocity of an object at a time and be the velocity of the same object at a time . If acceleration, , is known to be constant, then Note that velocity is a vector, so the magnitudes cannot be just subtracted in general.

If acceleration is not constant, then we can treat velocity as a function of time, . Then, at a particular instance,

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