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Is velocity:

  1. Distance/Time in a particular direction, or

  2. simply Displacement/Time?

Or both 1 and 2 is the same thing?

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migrated from math.stackexchange.com Jul 12 '13 at 12:48

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2  
It is $2$, when time is being squeezed to $0$. (We hope that the ratio vector stabilizes as the time interval is squeezed small enough.) –  Tunococ Jul 12 '13 at 12:30
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They are the same thing, infinitesimally. –  Neal Jul 12 '13 at 12:31
    
velocity is a vector hence it is in a particular direction , so 1) would fit. While in 2.) we have no information about the direction. –  Amire Bendjeddou Jul 12 '13 at 12:32
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@AmireBendjeddou Displacement indicates direction. –  Neal Jul 12 '13 at 12:42
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Try to look up khan academy video on this, or classical mechanics fall 1999 @ ocw.mit.edu. I say this because this is a very fundamental concept, and I think it will be better clarified if you try to study it from a book or any online resource. –  Saurabh Raje Jul 12 '13 at 17:16

3 Answers 3

up vote 1 down vote accepted

Instantaneous velocity is given by a small change in displacement over a small change in time, and it points in the direction in which you happen to be moving at the moment. Exactly what this means is a subtle point and essentially is why calculus was invented.

Your average velocity is given by the total displacement over a period of time divided by the time. The direction of average velocity is always the same as the direction of that displacement.

Speed is change in distance over change in time, and average speed is the total distance over the time it takes to cover that distance.

In general, average speed and average velocity are not the same thing, because distance and displacement are not the same thing. For example, suppose that you sprint across a room, and then sprint back to where you started. Your total displacement is $0$, which means your average velocity is $0$. The distance you cover is twice the length of the room, which means your average speed is non-zero and can be found as twice the length of the room divided by the time it took.

However, if you look at instantaneous velocity (the velocity you have at a given moment), then you instantaneous speed will always give you the magnitude of velocity, without the direction.

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2  
No, instantaneous velocity is a small change in location, not distance. Distance/time measures speed. –  Thomas Andrews Jul 12 '13 at 12:37
    
I flubbed the words in the first paragraph– meant to write displacement –  Omnomnomnom Jul 12 '13 at 13:05

Velocity is the time-derivative (that is, the current rate of change over time) of the location. Its length (called speed) gives the change in covered distance per time unit. Its direction shows the direction in which you move.

Note that the change in covered distance is not necessarily the change in distance from your starting point; for example, you may turn around, so your distance to the starting point decreases again. Your covered distance however continues to increase. In a car, the odometer shows the covered distance and the tachometer shows the current speed. Your GPS shows your current position. It also shows your current velocity, but usually split into magnitude (speed, displayed as number) and direction (displayed either as a fixed-length arrow on the map, or indirectly by rotating the map so that your direction is "up" on the map.

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Velocity is a VECTOR quantity. Speed is a scalar quantity. Both have dimensions of Lt^-1.

But velocity also has a direction; so a change of direction is a change of velocity, even if there is no change in speed. That is why orbiting objects, require a force (gravity) to keep on changing the direction of the velocity vector.

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