AoPSWiki
Visit the AoPS Book Store.

Acceleration

From AoPSWiki

Revision as of 17:12, 24 April 2009 by 5849206328x (Talk | contribs)
(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)

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 \textbf{v}_1 be the velocity of an object at a time t_1 and \textbf{v}_2 be the velocity of the same object at a time t_2. If acceleration, \textbf{a}, is known to be constant, then \textbf{a} = \frac{\textbf{v}_2 -\textbf{v}_1 }{t_2 - t_1} 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, v(t). Then, at a particular instance, \textbf{a} = \lim_{h\to 0} \frac{v(t+h)-v(t)}{(t+h)-t} = v'(t)

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

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Acceleration"
Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us