Average velocity independent of path taken

[dmission]

I'm having a hard time making sense of this in my head. I realize that the average velocity is displacement over time, and I get why displacement is the same as long as the starting and ending points are the same. But, what's confusing me is, say you fly in a straight line from LA to NY. Then, you flew from LA, down to Australia, then to NY. To do that in the same amount of time, wouldn't your speed have to be a LOT faster on average? I realize it's probably a dumb question, but it seems to me like that would change the average speed and therefore average velocity.

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[Axon hillock]

I'm having a hard time making sense of this in my head. I realize that the average velocity is displacement over time, and I get why displacement is the same as long as the starting and ending points are the same. But, what's confusing me is, say you fly in a straight line from LA to NY. Then, you flew from LA, down to Australia, then to NY. To do that in the same amount of time, wouldn't your speed have to be a LOT faster on average? I realize it's probably a dumb question, but it seems to me like that would change the average speed and therefore average velocity.

Speed is a scalar and therefore doesn't depend on direction. Thus speed is distance traveled/ time. Velocity is a vector and depends on direction. Therefore velocity has to be the displacement/ time. Try not to confuse speed and velocity.

 

[stsa84]

Yes, the plane that takes the longer route would have a much faster average speed than the plane that took the direct route, but their velocity would be the same. Think of speed as how quickly something is actually moving, and velocity of how quickly it is progressing towards it's destination.

Going 100 meters in a straight line in 10 seconds, gives an average speed of 10 m/s, and an average velocity of 10 m/s.

Going 100 meters by a winding route that covers 200 meters of actual distance in 10 seconds, gives an average speed of 20 m/s, but still an average velocity of 10 m/s.

Speed is quickness of movement, velocity is quickness of "progression from the start to the end point", if that makes it easier to get your mind around. Hope that helped.

 

[dmission]

Speed is a scalar and therefore doesn't depend on direction. Thus speed is distance traveled/ time. Velocity is a vector and depends on direction. Therefore velocity has to be the displacement/ time. Try not to confuse speed and velocity.

But doesn't velocity include speed and direction?

Yes, the plane that takes the longer route would have a much faster average speed than the plane that took the direct route, but their velocity would be the same. Think of speed as how quickly something is actually moving, and velocity of how quickly it is progressing towards it's destination.

Going 100 meters in a straight line in 10 seconds, gives an average speed of 10 m/s, and an average velocity of 10 m/s.

Going 100 meters by a winding route that covers 200 meters of actual distance in 10 seconds, gives an average speed of 20 m/s, but still an average velocity of 10 m/s.

Speed is quickness of movement, velocity is quickness of "progression from the start to the end point", if that makes it easier to get your mind around. Hope that helped.

And if the longer path plane also took longer to get there, then would it still have the same average velocity?

 

[Danlee07]

Oh... I get what you're getting confused on. You're thinking of speed and velocity as two completely separate things. They're not..it's not: speed changes, therefore velocity changes, it's: speeds changes and velocity changes...and no, the longer path taking longer time would result in a slower avg velocity