How Can You Linearize the Equation v=vw + (v0 - vw)e^-kt for Graphical Analysis?

[AlexLM]

Hi everyone!

I have an issue with my physical chemistry lab. They ask us to rearrange the fallowing equation

v=v_w + (v₀ - v_w)e^^-kt
where v is velocity and t is time, vw is a constant

They also ask which quantity would be plotted as ordinate and as absissa. We have to indicated the parameter of the slope and the intercept. Now once I have a equation I'll be able to find all those things but I can't seem to get to that equation.

I was thinking of plotting it for velocity and time. We also need to be able to figure out k from the graph

I tried for a while using the natural log of the function to lower the exponent and remove the e but I still can't seem to get a linear equation in which I'll be able to extract m and b.

As you can see I'm a chemistry student, not very good with anything physics related, and sorry for the broken English, it's my second language :)

Also sorry if this is in the wrong section, I'm new to this

 

[tiny-tim]

Welcome to PF!

Hi AlexLM! Welcome to PF!

Try writing it as v - v_w = (v₀ - v_w)e^-kt

(and btw, your English is fine )

 

[AlexLM]

Hi tiny-tim! Thanks a lot for the answer!

So basically if I graph for ln(v-v_w)=ln(v₀-v_w) -kt I could use ln(v-v_w) as my ordinate and t as my absissa. Then b would be ln(v₀-v_w) and the slope would be -k?

Does that make sense?

 

[tiny-tim]

yup!

(oh, and it's "abscissa", from the Latin "abscindere" )

 

[Chestermiller]

Hi tiny-tim! Thanks a lot for the answer!

So basically if I graph for ln(v-v_w)=ln(v₀-v_w) -kt I could use ln(v-v_w) as my ordinate and t as my absissa. Then b would be ln(v₀-v_w) and the slope would be -k?

Does that make sense?

If you do it on a semi-log plot, you don't actually have to calculate ln (v - v₀). Your graphics package should have semi-log plot capabilities.