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| 183_notes:displacement_and_velocity [2021/01/24 00:06] – [What's so special about constant velocity motion?] stumptyl | 183_notes:displacement_and_velocity [2021/02/18 21:16] – [Constant Velocity Motion] 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, | + | 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. |
| ==== Lecture Video ==== | ==== Lecture Video ==== | ||
| Line 15: | Line 15: | ||
| **Displacement** is a vector quantity that describes a change in position. | **Displacement** is a vector quantity that describes a change in position. | ||
| - | {{ course_planning: | + | {{ week1_constantv.png|Displacement vector}} |
| The displacement vector ($\Delta \vec{r}$) describes the change of an object' | The displacement vector ($\Delta \vec{r}$) describes the change of an object' | ||
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| + | \\ | ||
| === Average Velocity === | === Average Velocity === | ||
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| where $t_f - t_i$ is always positive, but $x_f-x_i$ can be positive, negative, or zero because it represents the displacement in the x-direction, | where $t_f - t_i$ is always positive, but $x_f-x_i$ can be positive, negative, or zero because it represents the displacement in the x-direction, | ||
| + | \\ | ||
| === Approximate Average Velocity === | === Approximate Average Velocity === | ||
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| //__This equation only hold exactly if the velocity changes linearly with time ([[183_notes: | //__This equation only hold exactly if the velocity changes linearly with time ([[183_notes: | ||
| + | |||
| + | \\ | ||
| === Instantaneous Velocity === | === Instantaneous Velocity === | ||
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| $$v_x = \lim_{\Delta t \rightarrow 0} \dfrac{\Delta x}{\Delta t} = \dfrac{dx}{dt}$$ | $$v_x = \lim_{\Delta t \rightarrow 0} \dfrac{\Delta x}{\Delta t} = \dfrac{dx}{dt}$$ | ||
| + | \\ | ||
| === Speed === | === Speed === | ||
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| $$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2}$$ | $$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2}$$ | ||
| - | Notice that the instantaneous velocity is equivalent to the magnitude of the velocity vector and, therefore, is a positive scalar quantity. | + | //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 ==== | ==== Predicting the motion of objects ==== | ||