183_notes:displacement_and_velocity

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183_notes:displacement_and_velocity [2021/01/24 00:38] – [Velocity and Speed] stumptyl183_notes:displacement_and_velocity [2021/02/18 21:17] (current) – [Velocity and Speed] stumptyl
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 ===== Constant Velocity Motion ===== ===== Constant Velocity Motion =====
  
-**Our job in mechanics is to predict or explain motion. So, all the models and tools that we develop are aimed at achieving this goal.**+//Our job in mechanics is to predict or explain motion. So, all the models and tools that we develop are aimed at achieving this goal.//
  
-The simplest model of motion is for an object that moves in a straight line at constant speed. You can use this simple model to build your understanding about the basic ideas of motion, and the different ways in which you will represent that motion. At the end of these notes, you will find the position update formula, which is a useful tool for predicting motion (particularly, when it comes to constant velocity motion).+The simplest model of motion is for an object that moves in a straight line at constant speed. You can use this simple model to build your understanding about the basic ideas of motion, and the different ways in which you will represent that motion. **At the end of these notes, you will find the position update formula, which is a useful tool for predicting motion (particularly, when it comes to constant velocity motion).**
  
 ==== Lecture Video ==== ==== Lecture Video ====
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 **Displacement** is a vector quantity that describes a change in position. **Displacement** is a vector quantity that describes a change in position.
  
-{{ course_planning:course_notes:displacement.png|Displacement vector}}+{{ week1_constantv.png|Displacement vector}}
 The displacement vector ($\Delta \vec{r}$) describes the change of an object's position in space (i.e., a change in location). So, you can think of the displacement vector as //displacement = change in position = final location - initial location//. This change in position is represented in the diagram to the right. Mathematically, we represent the displacement like this: The displacement vector ($\Delta \vec{r}$) describes the change of an object's position in space (i.e., a change in location). So, you can think of the displacement vector as //displacement = change in position = final location - initial location//. This change in position is represented in the diagram to the right. Mathematically, we represent the displacement like this:
  
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 /* Add a little about distance versus displacement */ /* Add a little about distance versus displacement */
-==== Velocity and Speed ====+===== Velocity and Speed =====
  
 **Velocity** is a vector quantity that describes the rate of change of the displacement. **Velocity** is a vector quantity that describes the rate of change of the displacement.
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 \\ \\
-=== Average Velocity ===+==== Average Velocity ====
  
 **Average Velocity** ($\vec{v}_{avg}$) describes how an object changes its displacement in a given time. To compute an object's average velocity, you will need the position of the object at two different times. You can think of it as //average velocity = displacement divided by time elapsed//. Mathematically, we can represent the average velocity like this: **Average Velocity** ($\vec{v}_{avg}$) describes how an object changes its displacement in a given time. To compute an object's average velocity, you will need the position of the object at two different times. You can think of it as //average velocity = displacement divided by time elapsed//. Mathematically, we can represent the average velocity like this:
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 \\ \\
  
-=== Approximate Average Velocity ===+==== Approximate Average Velocity ====
  
 The average velocity is defined as the displacement over a given time, but what about the //arithmetic// average velocity? How do the arithmetic average velocity and average velocity compare? The average velocity is defined as the displacement over a given time, but what about the //arithmetic// average velocity? How do the arithmetic average velocity and average velocity compare?
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 \\ \\
  
-=== Instantaneous Velocity ===+==== Instantaneous Velocity ====
  
 **Instantaneous velocity** ($\vec{v}$) describes how quickly an object is moving at a specific point in time. If you consider the displacement over shorter and shorter $\Delta t$'s, your computation will give a reasonable approximation for the instantaneous velocity. In the limit that $\Delta t$ goes to zero, your computation would be exact. Mathematically, we represent the instantaneous velocity like this: **Instantaneous velocity** ($\vec{v}$) describes how quickly an object is moving at a specific point in time. If you consider the displacement over shorter and shorter $\Delta t$'s, your computation will give a reasonable approximation for the instantaneous velocity. In the limit that $\Delta t$ goes to zero, your computation would be exact. Mathematically, we represent the instantaneous velocity like this:
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 \\ \\
  
-=== Speed ===+==== Speed ====
  
 **Speed** is a scalar quantity that describes that distance (not the displacement) traveled over an elapsed time. **Speed** is a scalar quantity that describes that distance (not the displacement) traveled over an elapsed time.
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