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course_planning:course_notes:constantv [2014/07/08 13:02] – caballero | course_planning:course_notes:constantv [2014/07/08 13:20] (current) – [Speed and Velocity] caballero | ||
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**Velocity: | **Velocity: | ||
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+ | === Average Velocity === | ||
Average Velocity (→vavg) describes how an object changes its displacement in a given time. To compute an object' | Average Velocity (→vavg) describes how an object changes its displacement in a given time. To compute an object' | ||
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where tf−ti is always positive, but xf−xi can be positive, negative, or zero because it represents the displacement in the x-direction, | where tf−ti is always positive, but xf−xi can be positive, negative, or zero because it represents the displacement in the x-direction, | ||
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+ | === Approximate Average Velocity === | ||
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+ | The average velocity is defined as the displacement over a given time, but what about the // | ||
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+ | The arithmetic average velocity is a approximation to the average velocity. | ||
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+ | vx,avg=ΔxΔt≈vix+vfx2 | ||
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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. | ||
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+ | === Instantaneous Velocity === | ||
Instantaneous velocity (→v) describes how quickly an object is moving a specific point in time. If you consider the displacement over shorter and shorter Δt's, your computation will give a reasonable approximation for the instantaneous velocity. In the limit that Δt goes to zero, your computation would be exact. Mathematically, | Instantaneous velocity (→v) describes how quickly an object is moving a specific point in time. If you consider the displacement over shorter and shorter Δt's, your computation will give a reasonable approximation for the instantaneous velocity. In the limit that Δt goes to zero, your computation would be exact. Mathematically, | ||
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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. | ||
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+ | === 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, | 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, | ||
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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 ==== | ||