# Difference between revisions of "Acceleration"

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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> | 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> | ||

+ | ==Useful Formulae== | ||

+ | Position and its time derivatives are often used in kinematics. For example, the following four equations relate the position <math>x</math>, velocity <math>v</math>, and (constant) acceleration <math>a</math> by magnitude: | ||

+ | <cmath> | ||

+ | \begin{align*} | ||

+ | x&=x_0+v_0t+\frac{1}{2}at^2 \\ | ||

+ | \Delta x&=\left(\frac{v+v_0}{2}\right)t \\ | ||

+ | v^2&=v_0^2+2a\Delta x \\ | ||

+ | \overline{v}&=\frac{v+v_0}{2}. | ||

+ | \end{align*} | ||

+ | </cmath> | ||

+ | By the chain rule, one can also show | ||

+ | <cmath>a=v\frac{\text{d} v}{\text{d}x}.</cmath> | ||

+ | Lastly, we have the famous formula of Newton relating the force and acceleration experienced by a massive object: | ||

+ | <cmath>\mathbf{F}=m\mathbf{a}.</cmath> | ||

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

[[Category:Definition]] | [[Category:Definition]] | ||

{{stub}} | {{stub}} |

## Latest revision as of 14:04, 24 April 2022

## 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,

## Useful Formulae

Position and its time derivatives are often used in kinematics. For example, the following four equations relate the position , velocity , and (constant) acceleration by magnitude: By the chain rule, one can also show Lastly, we have the famous formula of Newton relating the force and acceleration experienced by a massive object:

*This article is a stub. Help us out by expanding it.*