The time rate of change of velocity.
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Mathematical Definition
\begin
[ \vec
= \frac{d\vec{v}}
]\end
One-Dimensional Acceleration
Utility of the One-Dimensional Case
As with all vector equations, the equations of kinematics are usually approached by separation into components. In this fashion, the equations become three simultaneous one-dimensional equations. Thus, the consideration of motion in one dimension with acceleration can be generalized to the three-dimensional case.
Differential
\begin
$a = \frac
$\end
Graphical
Besides explicit acceleration graphs, acceleration can be found from the slope of a velocity vs. time graph or from the curvature (concavity) of a position vs. time graph.
Through Motion Diagrams
In a motion diagram, the acceleration can be estimated by looking at the spacing of the individual snapshots (assuming that the snapshots are separated by equal time intervals). If the spacing is increasing with time, the acceleration is in the direction of motion. If the spacing is decreasing with time, the acceleration is opposite to the direction of motion.