Question About Position, Velocity, etc. Fields

In summary, the textbook defines a velocity field as V = V(x,y,z,t) where x, y, and z are functions of time. This is because the function V() needs to know what time to evaluate the functions x(), y(), and z(), so the parameter t is necessary in the function's signature. This is similar to how programming languages require all parameters a function depends on to be included in its parameter list.
  • #1
Why in my textbook does it define a velocity field as V = V(x,y,z,t) where x, y, and z are functions of time.

I'm mixed up because if x, y, and z are functions of time, why does there need to be an additional time term t?
 
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  • #2
I think is an argument passing convention thing...have you done any programming?

I know that as a human, you can easily see that x depends on time t, but if you call a function V() and you only pass the x, y and z functions (of time) and do no pass the time...how is the function V() supposed to know what time to evaluate the functions x(), y(), z()? And so, you need to pass the scalar t, as well.
 
  • #3
gsal said:
I think is an argument passing convention thing...have you done any programming?

I know that as a human, you can easily see that x depends on time t, but if you call a function V() and you only pass the x, y and z functions (of time) and do no pass the time...how is the function V() supposed to know what time to evaluate the functions x(), y(), z()? And so, you need to pass the scalar t, as well.
I just...I don't even...Have you ever so far as to even go want if look more like?
 
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  • #4
I don't think you need a 't' in the brackets for all cases - for instance, where there is no acceleration. But, in general, the velocities may not be constant at all points x,y,z - so you need to specify the velocities at all points as they vary with time..
 
  • #5
ha!...I really lost you or you really never followed.

o.k. another shot at it.

If V() depends on x() and x() depends on t...does V() depend on t?

And so, when you write the signature of a function, you need to include in its parameter list all the parameters it depends on...and so V=V(x,y,z,t)
 

1. What is the difference between position and velocity fields?

Position fields refer to the physical location of an object in space, while velocity fields refer to the rate and direction of change in an object's position over time.

2. How are position, velocity, and acceleration related?

Position is the first derivative of velocity, and velocity is the first derivative of acceleration. In other words, acceleration describes how an object's velocity changes over time, and velocity describes how an object's position changes over time.

3. What is a vector field?

A vector field is a mathematical function that assigns a vector (such as position, velocity, or acceleration) to every point in space. It is often used to visualize and study the behavior of physical phenomena, such as the motion of a fluid or the electromagnetic field.

4. How do fields affect the behavior of particles or objects?

Fields exert forces on particles or objects that interact with them. For example, an electric field will exert a force on a charged particle, causing it to move in a certain direction.

5. Can fields be used to predict the future behavior of objects?

Yes, fields can be used to create mathematical models that can predict the future behavior of objects. This is often used in fields such as physics and engineering to design and optimize systems.

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