Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
| 183_notes:examples:positionpredict [2014/07/10 19:52] – 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 ===== | ===== 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> | ||
| + | |||
| + | 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 ==== | ==== 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 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. | * The motion of the cart is represented using the following motion diagram. | ||
| + | {{url> | ||
| ==== Solution ==== | ==== Solution ==== | ||
| Line 33: | Line 37: | ||
| We can compute the final location, | We can compute the final location, | ||
| - | $\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t = \vec{r}_i + \vec{v}_{cart} \Delta t = \vec{r}_i + \langle 1.2, 0, 0 \rangle \dfrac{m}{s} (3 s) = \vec{r}_i + \langle 3.6, 0, 0 \rangle m$ | + | $$\vec{r}_f = \vec{r}_i + \vec{v}_{avg} \Delta t = \vec{r}_i + \vec{v}_{cart} \Delta t = \vec{r}_i + \langle 1.2, 0, 0 \rangle \dfrac{m}{s} (3 s) = \vec{r}_i + \langle 3.6, 0, 0 \rangle m$$ |
| + | |||
| + | 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, | ||
| + | |||
| + | $$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0 \rangle m$$. | ||
| + | |||
| + | Notice that $y$-position of the cart remained unchanged because all the motion of the cart was in the $x$-direction. | ||