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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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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.

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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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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.

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I just...I don't even...Have you ever so far as to even go want if look more like?gsal said:

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.

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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)

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.

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.

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.

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.

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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