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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 | ||
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| ===== 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> | ||
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| + | 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 ==== | ||
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| * 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 ==== | ||
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| $$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0 \rangle m$$. | $$\vec{r}_f = \vec{r}_i + \langle 3.6, 0, 0 \rangle m = \langle 0.4, 1.1, 0 \rangle m + \langle 3.6, 0, 0 \rangle m = \langle 4.0, 1.1, 0 \rangle m$$. | ||
| - | Notice that $y$-position remained unchanged because all the motion of the cart was in the $x$-direction. | + | Notice that $y$-position |