course_planning:course_notes:constantv

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course_planning:course_notes:constantv [2014/07/08 13:02] – caballerocourse_planning:course_notes:constantv [2014/07/08 13:20] (current) – [Speed and Velocity] caballero
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 **Velocity:** A vector quantity that describes the rate of change of the displacement. **Velocity:** A vector quantity that describes the rate of change of the displacement.
 +
 +=== Average Velocity ===
  
 Average Velocity ($\vec{v}_{avg}$) describes how an object changes its displacement in a given time. To compute an object's average velocity, you will need the position of the object at two different times. You can think of it as //average velocity = displacement divided by time elapsed//. Mathematically, we can represent the average velocity like this: Average Velocity ($\vec{v}_{avg}$) describes how an object changes its displacement in a given time. To compute an object's average velocity, you will need the position of the object at two different times. You can think of it as //average velocity = displacement divided by time elapsed//. Mathematically, we can represent the average velocity like this:
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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, which is a vector component. 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, which is a vector component.
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 +
 +=== Approximate Average Velocity ===
 +
 +The average velocity is defined as the displacement over a given time, but what about the //arithmetic// average velocity? How do the arithmetic average velocity and average velocity compare?
 +
 +The arithmetic average velocity is a approximation to the average velocity.
 +
 +$$v_{x,avg} = \dfrac{\Delta x}{\Delta t} \approx \dfrac{v_{ix} + v_{fx}}{2}$$
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 +This equation only hold exactly if the velocity changes linearly with time (constant force motion). It might be a very poor approximation if velocity changes in other ways.
 +
 +=== Instantaneous Velocity ===
  
 Instantaneous velocity ($\vec{v}$) describes how quickly an object is moving a specific point in time. If you consider the displacement over shorter and shorter $\Delta t$'s, your computation will give a reasonable approximation for the instantaneous velocity. In the limit that $\Delta t$ goes to zero, your computation would be exact. Mathematically, we represent this instantaneous velocity like this: Instantaneous velocity ($\vec{v}$) describes how quickly an object is moving a specific point in time. If you consider the displacement over shorter and shorter $\Delta t$'s, your computation will give a reasonable approximation for the instantaneous velocity. In the limit that $\Delta t$ goes to zero, your computation would be exact. Mathematically, we represent this instantaneous velocity like this:
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 **Speed:** A scalar quantity that describes that distance (not the displacement) traveled over an elapsed time. **Speed:** A scalar quantity that describes that distance (not the displacement) traveled over an elapsed time.
 +
 +
 +=== Average speed ===
  
 Average speed ($s$) describes how quickly an object covers a given distance in a given amount of time. So, you can think of it as //average speed = total distance traveled divided by total time elapsed//. Mathematically, we represent the average speed like this: Average speed ($s$) describes how quickly an object covers a given distance in a given amount of time. So, you can think of it as //average speed = total distance traveled divided by total time elapsed//. Mathematically, we represent the average speed like this:
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 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.
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 ==== Predicting the motion of objects ==== ==== Predicting the motion of objects ====
  
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  • Last modified: 2014/07/08 13:02
  • by caballero