A really simple concept I’m struggling to understand.
What’s the difference between speed, and velocity?
I get one is scalar, one is a vector etc. But, I don’t understand how there’s a real difference.
I get one is scalar, one is a vector etc. But, I don’t understand how there’s a real difference.
Original post by Fhaidh846274
What’s the difference between speed, and velocity?
I get one is scalar, one is a vector etc. But, I don’t understand how there’s a real difference.
I get one is scalar, one is a vector etc. But, I don’t understand how there’s a real difference.
I drive 15 miles to a local town and then back home; it takes me an hour.
My average velocity is zero - I'm back where I started but my average speed is 30 mph.
Speed is dtance travelled/time but velocity is displacement [ie where I am compared to where I started]/time
Original post by Fhaidh846274
What’s the difference between speed, and velocity?
I get one is scalar, one is a vector etc. But, I don’t understand how there’s a real difference.
I get one is scalar, one is a vector etc. But, I don’t understand how there’s a real difference.
This is literally the difference - if you don't understand how there's a difference, you don't "get that one is a scalar and one is a vector". Speed is defined as the magnitude of the velocity vector.
(edited 1 year ago)
Original post by Muttley79
I drive 15 miles to a local town and then back home; it takes me an hour.
My average velocity is zero - I'm back where I started but my average speed is 30 mph.
Speed is dtance travelled/time but velocity is displacement [ie where I am compared to where I started]/time
My average velocity is zero - I'm back where I started but my average speed is 30 mph.
Speed is dtance travelled/time but velocity is displacement [ie where I am compared to where I started]/time
Oh! Thank you, that’s really helpful. I understand
Original post by Plagioclase
This is literally the difference - if you don't understand how there's a difference, you don't "get that one is a scalar and one is a vector". Speed is defined as the magnitude of the velocity vector.
How does that work in my example?
Original post by Plagioclase
This is literally the difference - if you don't understand how there's a difference, you don't "get that one is a scalar and one is a vector". Speed is defined as the magnitude of the velocity vector.
You’ve just repeated my post back to me. I was asking for an explanation as to what that means, I can repeat the textbook, as you’ve done, but that doesn’t mean I understand how that acts in the real world, but the above kindly explained. Thanks anyway.
Original post by Muttley79
How does that work in my example?
Taking the vector magnitude is a nonlinear operation. The magnitude of the mean of a set of vectors is not equal to the mean of the magnitude of a set of vectors.
Original post by Plagioclase
Taking the vector magnitude is a nonlinear operation. The magnitude of the mean of a set of vectors is not equal to the mean of the magnitude of a set of vectors.
And in English? I don't think it's helpful to just quote textbooks
Original post by Plagioclase
Taking the vector magnitude is a nonlinear operation. The magnitude of the mean of a set of vectors is not equal to the mean of the magnitude of a set of vectors.
That’s not particularly helpful, it’s almost exactly what the textbook says, which is why I came here, as I was unsure what that meant. It doesn’t make you seem smarter being able to over-complicate something, I was after a simple response to make it easier to understand.
From what I understand, velocity is the ‘quickness’, speed is the distance traveled in a certain amount of time (ie. Metres in 1 second).
Original post by Fhaidh846274
That’s not particularly helpful, it’s almost exactly what the textbook says, which is why I came here, as I was unsure what that meant. It doesn’t make you seem smarter being able to over-complicate something, I was after a simple response to make it easier to understand.
From what I understand, velocity is the ‘quickness’, speed is the distance traveled in a certain amount of time (ie. Metres in 1 second).
From what I understand, velocity is the ‘quickness’, speed is the distance traveled in a certain amount of time (ie. Metres in 1 second).
You wrote in your original post that you understand that speed is a scalar and that velocity is a vector, but you don't understand the 'real difference'. That is the difference. If you don't understand the difference, that means you don't understand what scalars and vectors are.
If something is in motion, its position is changing through time. "Velocity" is the complete description of the rate of change of an object's position. Position is a vector (if you're in three dimensional space, your position is a three dimensional vector) and therefore velocity is also a vector, because it tells you the rate of change of position. Speed is simply the magnitude of the velocity vector.
If I'm in three dimensional space, I can describe my position with a vector s = (x, y, z), which let's say has units of metres. If my x position is decreasing at a rate of 1 metre per second, my velocity is v = (-1, 0, 0) m s-1. To work out my speed, I just have to find the magnitude of that vector, which is ((-1)2 + 02 + 02)0.5 = 1 m s-1. The speed doesn't give us any information about where we're moving, it just tells us how rapidly our position is changing. If I told you that my speed was 1 m s-1, you would know how quickly I'm moving through space, but you wouldn't know what direction I'm moving in. If I told you that my velocity was (-1, 0, 0) m s-1, you'd know how quickly I'm moving through space (by working out the magnitude of that vector) but you'd also know where I'm moving (towards the negative x direction). If my velocity now changes to v = (0, 1, 0) m s-1, my speed is exactly the same as before (1 m s-1), but I'm moving in a completely different direction (towards the positive y direction).
(edited 1 year ago)
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