Calculating Velocity: Find v from K_M Eqn

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In summary, the conversation is about finding the velocity of a Lorentz violating wavepacket, which is represented by the equation [tex\\begin{equation}\langle\varphi(t,x)\rangle \equiv\exp\Bigg[i\textbf{K}_M(t-x)-\frac{\Delta\textbf{K}_M}{4}(t-x)^2\Bigg]\end{equation}[/tex]. The velocity is calculated using the first term in the exponent and is given by v=k_0+\frac{k_0^3}{2M^2}t(1+t-x).
  • #1
smallgirl
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1. Hey,

so I have a Lorentz violating wavepacket and from this I need to find the velocity.


My wavepacket is of the form

[tex\\begin{equation}
\langle\varphi(t,x)\rangle \equiv\exp\Bigg[i\textbf{K}_M(t-x)-\frac{\Delta\textbf{K}_M}{4}(t-x)^2\Bigg]
\end{equation}[/tex]

where for this question you need to know that

[tex]K_M=k_0+\frac{t}{2M^2}K_0^3[/tex]

I did this:

[tex]
K_m(dt-dx)=k_0(dt-dx)+\frac{k_0^3}{2M^2}(t(dt-dx)+(t-x)dt)[/tex]

I only need to calculate v from the first term in the exponent and dt=dx and v=dx/dt and it must be of the form 1+...
 
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  • #2
v=k_0+\frac{k_0^3}{2M^2}t(dt-dx)v=k_0+\frac{k_0^3}{2M^2}t(dt-dx)=k_0+\frac{k_0^3}{2M^2}t(1+t-x)Thus, the velocity of the wavepacket is given by:v=k_0+\frac{k_0^3}{2M^2}t(1+t-x)
 

FAQ: Calculating Velocity: Find v from K_M Eqn

What is the equation for calculating velocity using the K_M equation?

The equation for calculating velocity using the K_M equation is v = (V_max [S])/(K_m + [S]), where v is the velocity, V_max is the maximum velocity, K_m is the Michaelis-Menten constant, and [S] is the substrate concentration.

What is V_max and K_m in the K_M equation?

V_max is the maximum velocity, which is the maximum rate of reaction that can be achieved at high substrate concentrations. K_m is the Michaelis-Menten constant, which is a measure of the affinity of the enzyme for the substrate.

How do you determine the value of V_max and K_m in the K_M equation?

The values of V_max and K_m can be determined experimentally by measuring the initial reaction rate at various substrate concentrations and then plotting the data on a Lineweaver-Burk plot. The slope of the line gives the value of V_max, and the x-intercept gives the value of K_m.

What is the relationship between substrate concentration and velocity in the K_M equation?

In the K_M equation, as the substrate concentration increases, the velocity initially increases, but eventually levels off at V_max. This is because at high substrate concentrations, all of the enzyme active sites are saturated with substrate, so the velocity cannot increase any further.

What are the limitations of using the K_M equation to calculate velocity?

The K_M equation assumes that the reaction is following Michaelis-Menten kinetics, which is not always the case. It also assumes that the reaction is taking place under ideal conditions, such as a constant temperature and pH. Additionally, measuring accurate values for V_max and K_m can be difficult in practice.

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