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--- 183_notes:examples:positionpredict [2014/07/10 19:56] – [Solution] caballero
+++ 183_notes:examples:positionpredict [2024/01/31 16:37] (current) – [Setup] caballero
@@ Line 3: / Line 3: @@
 ===== Example: Predicting the location of a object undergoing constant velocity motion =====
-A cart is given a slight push along a near frictionless track (as shown in the video below). After the push, the cart is observed to move with a near constant velocity  $\vec{v}_{cart} =\langle 1.2, 0, 0 \rangle \dfrac{m}{s}$ . Determine its location after 3 seconds.
+A cart is given a slight push along a near frictionless track (as shown in the video below).
+{{ youtube>sdjsaxLfevQ?large }}
+After the push, the cart is observed to move with a near constant velocity  $\vec{v}_{cart} =\langle 1.2, 0, 0 \rangle \dfrac{m}{s}$ . Determine its location after 3 seconds.
 ==== Setup ====
@@ Line 28: / Line 31: @@
   * The location of the cart can be predicted using the position update formula,  $\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t$
   * The motion of the cart is represented using the following motion diagram.
+{{url>https://glowscript.org/#/user/danny/folder/Shared/program/FanCarConstantVelocity 660px,420px|Simulation of Fan Cart moving with Constant Velocity}}
 ==== Solution ====
@@ Line 35: / Line 39: @@
  $\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t = \vec{r}_i + \vec{v}_{cart} \Delta t = \vec{r}_i + \langle 1.2, 0, 0 \rangle \dfrac{m}{s} (3 s) = \vec{r}_i + \langle 3.6, 0, 0 \rangle m$
-You might use the video to define an origin such that the initial position of the cart is  $\vec{r}_i = \langle 0.4, 1.1, 0 \rangle m$ . With that new information, the final location of the cart can be computed,
+You might use the video to define an origin such that the initial position of the cart is  $\vec{r}_i = \langle 0.4, 1.1, 0 \rangle m$ . With that new information, the final location of the cart can be computed exactly,
-$$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0, \rangle m$$.
+ $\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0 \rangle m$ .
-Notice that  $y$ -position remained unchanged because all the motion of the cart was in the  $x$ -direction.
+Notice that  $y$ -position of the cart remained unchanged because all the motion of the cart was in the  $x$ -direction.