Section 2.3 Velocity
Subsubsection Key Ideas
Velocity is the quantity that will tell you both how fast an object is moving and the direction in which it is moving. Furthermore, velocity is the rate of change at which the position of the object is changing in time.
Definition 2.3.2. Average Velocity.
The average velocity of an object is the object’s displacement divided by the interval of time required to move through that displacement:
\begin{equation*}
\vec{v}_{ave} = \frac{\Delta \vec{r}}{\Delta t}
\end{equation*}
Note 2.3.3. Speed vs. Velocity.
When speaking to a friend or colleague you may not make a distinction between speed and velocity, but in physics the words are distinct. Where velocity is a vector, indicating both magnitude and direction, the word speed refers only to the magnitude of the velocity.
Subsubsection Activities
Activity 2.3.1. Summarize What You Learned - Velocity.
Write a 1-2 sentence description of what the definition of average velocity says in words.
Activity 2.3.2. Sensemaking: Units.
What are the units of velocity? Explain how these units are consistent with the units of the other quantities in the definition of average velocity given above.
Explanation 2.3.3. Direction of Velocity.
How does the direction of the average velocity vector compare to the direction of the displacement vector? Explain your reasoning using the Explanation Task Steps.
Activity 2.3.4. Finding Average Velocity.
Sketch the vector corresponding to the average velocity between instant 1 and instant 9 in the video lesson above.
Subsubsection Instantaneous Velocity
Video Lesson 2.3.5. Instantaneous Velocity.
Physics distinguishes between average quantities for intervals of definite time, and instantaneous quantities for infinitesimal intervals. To signal the difference, you will use the symbol \(d\) for an infinitesimal quantity instead of the \(\Delta\) symbol that you use for a non-infinitesimal change.
Definition 2.3.6. Instantaneous Velocity.
The instantaneous velocity of an object is found by taking the limit as \(\Delta t \rightarrow 0\text{,}\) resulting in infinitesimal changes in position and time:
\begin{equation*}
\vec{v} = \frac{d \vec{r}}{d t}
\end{equation*}
Note that when you make this change in notation, the velocity suddenly becomes a derivative!
