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--- course_planning:course_notes:constantv [2014/06/22 07:25] – pwirving
+++ course_planning:course_notes:constantv [2014/07/08 13:02] – caballero
@@ Line 1: / Line 1: @@
-===== The Constant Velocity Model =====
+===== 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.
+Our job in mechanics is to predict 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).
 ==== Motion (Changes of Position) ====
@@ Line 57: / Line 59: @@
 Notice that the instantaneous velocity is equivalent to the magnitude of the velocity vector and, therefore, is a positive scalar quantity.
+==== Predicting the motion of objects ====
+We can rewrite the definition of average velocity above to give us information about the displacement of an object,
+$$ \Delta \vec{r} = \vec{r}_f - \vec{r}_i = \vec{v}_{avg} \Delta t$$
+This equation tells us that given a certain average velocity ($\vec{v}_{avg}$) over a known time interval ($\Delta t$), an object will experience a particular displacement ($\Delta \vec{r}$). By moving the initial position over to the left side, we get the "position update" formula,
+$$ \vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t $$
+which allows us to predict the location of an object given its initial position and average motion. This formula is a very powerful because it allows us to predict where an object will be given only information about it now.
 ==== What's so special about constant velocity motion? ====
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 $$\vec{v}_{avg} = \vec{v}$$
-The object changes its position at a constant rate.
+The object changes its position at a constant rate. In the position update formula, we can replace the average velocity with simply the instantaneous velocity,
+$$ \vec{r}_f = \vec{r}_i + \vec{v} \Delta t $$
 ==== Pre-Lecture - Displacement and Velocity ====
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