Turning a vector into a vector function of time

[Timothy S]

Homework Statement

[/B]
A Velocity vector: V = (12,4)

write the vector as a vector function of Displacement.

2. The attempt at a solution

I integrated the components of the Vector and got the function S(t) = (S(12t), S(4t))

I this correct at all?

 

[Ray Vickson]

Homework Statement

[/B]
A Velocity vector: V = (12,4)

write the vector as a vector function of Displacement.

2. The attempt at a solution

I integrated the components of the Vector and got the function S(t) = (S(12t), S(4t))

I this correct at all?

This cannot be answered because the notation S(12t), etc., is undefined.

 

[Timothy S]

why?

 

[Ray Vickson]

why?

Why what?
(1) Why the notation is undefined? The answer is: because you have not defined it.
(2) Why I can't answer the question? Because---as I have already said---I have no idea what you mean by what you wrote.

 

[Mark44]

I integrated the components of the Vector and got the function S(t) = (S(12t), S(4t))

Do you mean S(t) = <12t, 4t>?
If so, don't forget you need the constant of integration.

 

[Timothy S]

Ray, I asked why because I literally have no idea what I'm talking about.

Mark, from V = 12x + 4y, am i allowed to turn it into that function that you wrote.

 

[mfb]

Homework Statement

[/B]
A Velocity vector: V = (12,4)

write the vector as a vector function of Displacement.

Is this the exact and full problem statement? It sounds a bit odd.

 

[Timothy S]

I made it up myself.

 

[mfb]

I don't think it makes sense.

 

[Ray Vickson]

Ray, I asked why because I literally have no idea what I'm talking about.

Mark, from V = 12x + 4y, am i allowed to turn it into that function that you wrote.

You say you literally have no idea what you are talking about. So, let's look at that.


If you are told a function f(t) for x-displacement, say x = f(t), can you figure out from that how to obtain velocity? Can you go backwards: given a velocity function g(t), so that v = g(t), can you figure out from that how to get displacement x = f(t)? [In a nutshell, that is what you are being asked to do in this problem.]


If the answers to both (or even one) of these questions is NO, you need to upgrade your background. You can Google “displacement and velocity” to find numerous articles on these issues.

 

[Timothy S]

Wait a minute.

I can breakup the vector into:

V_x = 12

and

V_y = 4

these can easy be described as a function. a constant function of velocity. I can find the integral of the function V(t) = 12, and turn it into S(t) = 12t

 

[Timothy S]

and furthermore, from S(x) = x, which is a function of displacement, I CAN find the function for instantaneous velocity by simply finding the derivative. The answer is, it has no velocity as the function is constant.

 

[Mark44]

Mark, from V = 12x + 4y, am i allowed to turn it into that function that you wrote.

You could have V(t) = 12i + 4j, which would be the same as V(t) = <12, 4>. i and j are the unit vectors in the direction of the positive x- and y-axes.

Wait a minute.

I can breakup the vector into:

V_x = 12

and

V_y = 4

these can easy be described as a function. a constant function of velocity. I can find the integral of the function V(t) = 12, and turn it into S(t) = 12t

Is this a different example? Above you have V_x = 12, and now you have V(t) = 12. This would be incorrect if V(t) = <12, 4>.

If you really mean V_x(t), the x-component of velocity, then S_x(t) = 12t + C₁. As I said before, you have to add the constant of integration.

and furthermore, from S(x) = x, which is a function of displacement, I CAN find the function for instantaneous velocity by simply finding the derivative. The answer is, it has no velocity as the function is constant.

This makes no sense. If you're talking about displacement and velocity, the independent variable should be t, not x. Having said that, if S(x) = x, then S'(x) = 1 represents the "velocity" here, a constant velocity, which is not the same as "no velocity."

 

[Timothy S]

I get what your saying. S(x) = x was meant to be a position function. The point is i wanted to turn the velocity vector into a function. that's all. I didn't know if that's even possible.

 

[Mark44]

I get what your saying. S(x) = x was meant to be a position function. The point is i wanted to turn the velocity vector into a function. that's all. I didn't know if that's even possible.

V(t) = <12, 4> is a vector-valued function, albeit one that produces a vector constant. Or in slightly different form, V(t) = 12i + 4j.