Section 2.10 Acceleration
The term acceleration describes the rate of change of an object’s velocity. Like velocity (the rate of change of an object’s position), acceleration can be either average (involving large changes written using \(\Delta\)) or instantaneous (involving small, infinitesimal changes written using \(d\)).
Definition 2.10.1. Average Acceleration.
The average acceleration of an object is the object’s change in velocity divided by the interval of time required to change the velocity:
\begin{equation*}
\vec{a}_{ave} = \frac{\Delta \vec{v}}{\Delta t}
\end{equation*}
Definition 2.10.2. Instantaneous Acceleration.
The instantaneous acceleration of an object is given by
\begin{equation*}
\vec{a} = \frac{d \vec{v}}{d t}
\end{equation*}
Exercises Activities
1. Summarize What You Learned - Acceleration.
Write a 1-2 sentence description of what the definition of acceleration says in words.
2. Sensemaking: Units.
What are the units of acceleration? Explain how these units are consistent with the units of other quantities you have learned about.
3. Explanation: Direction.
How does the direction of the average acceleration vector compare to the direction of the change in velocity vector?
Tip.
Does acceleration have to point in the same direction as velocity?
Answer.
The average acceleration vector points in the same direction as the change in velocity!
